title: Gender inequality

text: Prenatal hormone exposure influences the extent to which a person exhibits typical masculine or feminine traits. Negligible differences between males and females exist in general intelligence. Women are significantly less likely to take risks than men. Men are also more likely than women to be aggressive, a trait influenced by prenatal and possibly current androgen exposure. It has been theorized that these differences combined with physical differences are an adaptation representing sexual division of labour. A second theory proposes sex differences in intergroup aggression represent adaptations in male aggression to allow for territory, resource and mate acquisition. Females are (on average) more empathetic than males, though this does not mean that any given woman is more empathetic than any given man. Men and women have better visuospatial and verbal memory, respectively. These changes are influenced by the male sex hormone testosterone, which increases visuospatial memory in both genders when administered.


title: Gender inequality

text: From birth, males and females are socialised differently, and experience different environments throughout their lives. Due to societal influence, gender often greatly influences many major characteristics in life; such as personality. Males and females are led on different paths due to the influences of gender role expectations and gender role stereotypes often before they are able to choose for themselves. For instance, in Western societies,the colour blue is commonly associated with boys, and they are often given toys that are associated with traditional masculine roles, such as machines and trucks. Girls are associated with the colour pink, and are given toys related to traditional feminine roles, such as dolls, dresses, and dollhouses. These influences by parents or other adult figures in the child's life encourage them to fit into these roles. This tends to affect personality, career paths, or relationships. Throughout life, males and females are seen as two very different species who have very different personalities and should stay on separate paths.


title: Gender inequality

text: Researcher Janet Hyde found that, although much research has traditionally focused on the differences between the genders, they are actually more alike than different, which is a position proposed by the gender similarities hypothesis.


title: Gender inequality

text: Across the board, a number of industries are stratified across the genders. This is the result of a variety of factors. These include differences in education choices, preferred job and industry, work experience, number of hours worked, and breaks in employment (such as for bearing and raising children). Men also typically go into higher paid and higher risk jobs when compared to women. These factors result in 60% to 75% difference between men's and women's average aggregate wages or salaries, depending on the source. Various explanations for the remaining 25% to 40% have been suggested, including women's lower willingness and ability to negotiate salary and sexual discrimination. According to the European Commission direct discrimination only explains a small part of gender wage differences.


title: Gender inequality

text: In the United States, the "average" female's "unadjusted" annual salary has been cited as 78% of that of the "average" male. However, multiple studies from OECD, AAUW, and the US Department of Labor have found that pay rates between males and females varied by 5–6.6% or, females earning 94 cents to every dollar earned by their male counterparts, when wages were adjusted to different individual choices made by male and female workers in college major, occupation, working hours, and maternal/parental leave. The remaining 6% of the gap has been speculated to originate from deficiency in salary negotiating skills and sexual discrimination.


title: Gender inequality

text: Human capital theories refer to the education, knowledge, training, experience, or skill of a person which makes them potentially valuable to an employer. This has historically been understood as a cause of the gendered wage gap but is no longer a predominant cause as women and men in certain occupations tend to have similar education levels or other credentials. Even when such characteristics of jobs and workers are controlled for, the presence of women within a certain occupation leads to lower wages. This earnings discrimination is considered to be a part of pollution theory. This theory suggests that jobs which are predominated by women offer lower wages than do jobs simply because of the presence of women within the occupation. As women enter an occupation, this reduces the amount of prestige associated with the job and men subsequently leave these occupations. The entering of women into specific occupations suggests that less competent workers have begun to be hired or that the occupation is becoming deskilled. Men are reluctant to enter female-dominated occupations because of this and similarly resist the entrance of women into male-dominated occupations.


title: Gender inequality

text: The gendered income disparity can also be attributed in part to occupational segregation, where groups of people are distributed across occupations according to ascribed characteristics; in this case, gender. Occupational gender segregation can be understood to contain two components or dimensions; horizontal segregation and vertical segregation. With horizontal segregation, occupational sex segregation occurs as men and women are thought to possess different physical, emotional, and mental capabilities. These different capabilities make the genders vary in the types of jobs they are suited for. This can be specifically viewed with the gendered division between manual and non-manual labor. With vertical segregation, occupational sex segregation occurs as occupations are stratified according to the power, authority, income, and prestige associated with the occupation and women are excluded from holding such jobs.


title: Gender inequality

text: As women entered the workforce in larger numbers since the 1960s, occupations have become segregated based on the amount femininity or masculinity presupposed to be associated with each occupation. Census data suggests that while some occupations have become more gender integrated (mail carriers, bartenders, bus drivers, and real estate agents), occupations including teachers, nurses, secretaries, and librarians have become female-dominated while occupations including architects, electrical engineers, and airplane pilots remain predominately male in composition. Based on the census data, women occupy the service sector jobs at higher rates than men. Women's overrepresentation in service sector jobs, as opposed to jobs that require managerial work acts as a reinforcement of women and men into traditional gender roles that causes gender inequality.


title: Gender inequality

text: "The gender wage gap is an indicator of women's earnings compared with men's. It is figured by dividing the average annual earnings for women by the average annual earnings for men." (Higgins et al., 2014)


title: Gender inequality

text: Scholars disagree about how much of the male-female wage gap depends on factors such as experience, education, occupation, and other job-relevant characteristics. Sociologist Douglas Massey found that 41% remains unexplained, while CONSAD analysts found that these factors explain between 65.1 and 76.4 percent of the raw wage gap. CONSAD also noted that other factors such as benefits and overtime explain "additional portions of the raw gender wage gap".


title: Gender inequality

text: The glass ceiling effect is also considered a possible contributor to the gender wage gap or income disparity. This effect suggests that gender provides significant disadvantages towards the top of job hierarchies which become worse as a person's career goes on. The term glass ceiling implies that invisible or artificial barriers exist which prevent women from advancing within their jobs or receiving promotions. These barriers exist in spite of the achievements or qualifications of the women and still exist when other characteristics that are job-relevant such as experience, education, and abilities are controlled for. The inequality effects of the glass ceiling are more prevalent within higher-powered or higher income occupations, with fewer women holding these types of occupations. The glass ceiling effect also indicates the limited chances of women for income raises and promotion or advancement to more prestigious positions or jobs. As women are prevented by these artificial barriers, from either receiving job promotions or income raises, the effects of the inequality of the glass ceiling increase over the course of a woman's career.


title: Gender inequality

text: Statistical discrimination is also cited as a cause for income disparities and gendered inequality in the workplace. Statistical discrimination indicates the likelihood of employers to deny women access to certain occupational tracks because women are more likely than men to leave their job or the labor force when they become married or pregnant. Women are instead given positions that dead-end or jobs that have very little mobility.


title: Gender inequality

text: In developing countries such as the Dominican Republic, female entrepreneurs are statistically more prone to failure in business. In the event of a business failure women often return to their domestic lifestyle despite the absence of income. On the other hand, men tend to search for other employment as the household is not a priority.


title: Gender inequality

text: The gender earnings ratio suggests that there has been an increase in women's earnings comparative to men. Men's plateau in earnings began after the 1970s, allowing for the increase in women's wages to close the ratio between incomes. Despite the smaller ratio between men and women's wages, disparity still exists. Census data suggests that women's earnings are 71 percent of men's earnings in 1999.


title: Gender inequality

text: The gendered wage gap varies in its width among different races. Whites comparatively have the greatest wage gap between the genders. With whites, women earn 78% of the wages that white men do. With African Americans, women earn 90% of the wages that African American men do.


title: Gender inequality

text: There are some exceptions where women earn more than men: According to a survey on gender pay inequality by the International Trade Union Confederation, female workers in the Gulf state of Bahrain earn 40 percent more than male workers.


title: Gender inequality

text: In 2014, a report by the International Labor Organization (ILO) reveals the wage gap between Cambodian women factory workers and other male counterparts. There was a US$25 monthly pay difference, suggesting that women have a much lower power and being devalued not only at home but also in the workplace.


title: Gender inequality

text: The gender gap has narrowed to various degrees since the mid-1960s. Where some 5% of first-year students in professional programs were female in 1965, by 1985 this number had jumped to 40% in law and medicine, and over 30% in dentistry and business school. Before the highly effective birth control pill was available, women planning professional careers, which required a long-term, expensive commitment, had to "pay the penalty of abstinence or cope with considerable uncertainty regarding pregnancy". This control over their reproductive decisions allowed women to more easily make long-term decisions about their education and professional opportunities. Women are highly underrepresented on boards of directors and in senior positions in the private sector.


title: Gender inequality

text: Additionally, with reliable birth control, young men and women had more reason to delay marriage. This meant that the marriage market available to any women who "delay[ed] marriage to pursue a career ... would not be as depleted. Thus the Pill "could" have influenced women's careers, college majors, professional degrees, and the age at marriage."


title: Gender inequality

text: Studies on sexism in science and technology fields have produced conflicting results. Moss-Racusin et al. found that science faculty of both sexes rated a male applicant as significantly more competent and hireable than an identical female applicant. These participants also selected a higher starting salary and offered more career mentoring to the male applicant. Williams and Ceci, however, found that science and technology faculty of both sexes "preferred female applicants 2:1 over identically qualified males with matching lifestyles" for tenure-track positions. Studies show parents are more likely to expect their sons, rather than their daughters, to work in a science, technology, engineering or mathematics field – even when their 15-year-old boys and girls perform at the same level in mathematics. There are more men than women trained as dentists, this trend has been changing.


title: Gender inequality

text: A survey by the U.K. Office for National Statistics in 2016 showed that in the health sector 56% of roles are held by women, while in teaching it is 68%. However equality is less evident in other area; only 30% of M.P.s are women and only 32% of finance and investment analysts. In the natural and social sciences 43% of employees are women, and in the environmental sector 42%.


title: Gender inequality

text: In an article by MacNell et al. (2014), researchers used an online course and falsified the names of assistant teachers to make students believe they had either a female or a male teaching assistant. At the end of the semester, they had the students complete a course evaluation. Regardless of whether the teaching assistant was actually male or female, assistants who were perceived as female received lower course evaluations overall with distinctly lower ratings in areas of promptness, praise, fairness, and professionalism.


title: Gender inequality

text: In an article titled "Gender Differences in Education, Career Choices and Labor Market Outcomes on a Sample of OECD Countries", the researchers focused their work on how both men and women differ from their studies, their focuses, and their objectives within their work. Women are seen to have higher chances to choose the humanities and health fields while decreasing their opportunities in the sciences and social sciences fields. This indicates that there is a larger impact on men's decisions about fields of study.


title: Gender inequality

text: A 2010 study conducted by David R. Hekman and colleagues found that customers, who viewed videos featuring a black male, a white female, or a white male actor playing the role of an employee helping a customer, were 19 percent more satisfied with the white male employee's performance.


title: Gender inequality

text: This discrepancy with race can be found as early as 1947, when Kenneth Clark conducted a study in which black children were asked to choose between white and black dolls. White male dolls were the ones children preferred to play with.


title: Gender inequality

text: Gender inequalities still exist as social problems and are still growing in places. In 2008, recently qualified female doctors in New York State had a starting salary $16,819 less than their male counterparts. An increase compared to the $3,600 difference of 1999. The pay discrepancy could not be explained by specialty choice, practice setting, work hours, or other characteristics. Nonetheless, some potentially significant factors like family or marital status were not evaluated. A case study carried out on Swedish medical doctors showed that the gender wage gap among physicians was greater in 2007 than in 1975.


title: Gender inequality

text: Wage discrimination is when an employer pays different wages to two seemingly similar employees, usually on the basis of gender or race. Kampelmann and Rycx (2016) explain two different explanations for the differences observed in wages. They explain that employer tastes and preferences for foreign workers and/or customers can translate into having a lower demand for them as a whole and as a result offering them lower wages, as well as the differences in career dynamics, whereas, if there is large differences between immigrant workers and "native" workers, it could lead to wage discrimination for immigrant workers. Within the discrimination of domestic to foreign workers there is also discrimination among foreign workers based on gender. Female migrant workers are faced with a "triple-discrimination". This "triple-discrimination" states that women foreign workers are more at risk to experience discrimination because they are women, unprotected workers, and migrant workers.


title: Gender inequality

text: Gender roles are heavily influenced by biology, with male-female play styles correlating with sex hormones, sexual orientation, aggressive traits, and pain. Furthermore, females with congenital adrenal hyperplasia demonstrate increased masculinity and it has been shown that rhesus macaque children exhibit preferences for stereotypically male and female toys.


title: Gender inequality

text: Gender inequality in relationships has been growing over the years but for the majority of relationships, the power lies with the male. Even now men and women present themselves as divided along gender lines. A study done by Szymanowicz and Furnham, looked at the cultural stereotypes of intelligence in men and women, showing the gender inequality in self-presentation. This study showed that females thought if they revealed their intelligence to a potential partner, then it would diminish their chance with him. Men however would much more readily discuss their own intelligence with a potential partner. Also, women are aware of people's negative reactions to IQ, so they limit its disclosure to only trusted friends. Females would disclose IQ more often than men with the expectation that a real true friend would respond in a positive way. Intelligence continues to be viewed as a more masculine trait, than feminine trait. The article suggested that men might think women with a high IQ would lack traits that were desirable in a mate such as warmth, nurturance, sensitivity, or kindness. Another discovery was that females thought that friends should be told about one's IQ more so than males. However, males expressed doubts about the test's reliability and the importance of IQ in real life more so than women. The inequality is highlighted when a couple starts to decide who is in charge of family issues and who is primarily responsible for earning income. For example, in Londa Schiebinger's book, "Has Feminism Changed Science?", she claims that "Married men with families on average earn more money, live longer and happier, and progress faster in their careers", while "for a working woman, a family is a liability, extra baggage threatening to drag down her career." Furthermore, statistics had shown that "only 17 percent of the women who are full professors of engineering have children, while 82 percent of the men do."


title: Gender inequality

text: Despite the increase in women in the labor force since the mid-1900s, traditional gender roles are still prevalent in American society. Many women are expected to put their educational and career goals on hold in order to raise a family, while their husbands become primary breadwinners. However, some women choose to work and also fulfill a perceived gender role of cleaning the house and caring for children. Despite the fact that certain households might divide chores more evenly, there is evidence supporting the issue that women have continued being the primary care-giver in family life even if they work full-time jobs. This evidence suggests that women who work outside the home often put an extra 18 hours a week doing household or childcare related chores as opposed to men who average 12 minutes a day in childcare activities. One study by van Hooff showed that modern couples, do not necessarily purposefully divide things like household chores along gender lines, but instead may rationalize it and make excuses. One excuse used is that women are more competent at household chores and have more motivation to do them, and some say the jobs men have are much more demanding.


title: Gender inequality

text: In "The Unsettling of America: Culture and Agriculture", Wendell Berry wrote in the 1970s that the "home became a place for the husband to go when he was not working ... it was the place where the wife was held in servitude." A study conducted by Sarah F. Berk, called "The Gender Factory", researched this aspect of gender inequality as well. Berk found that "household labor is about power". The reason the spouse performing less housework is not the spouse in power is simple; they have more free time than their counterpart; therefore, they are able to do more of what they want after the average workday.


title: Gender inequality

text: Gender roles have changed drastically over the past few decades. In an article taking the time period of 1920–1966, data was recorded which surmised that women spent most of their time tending the home and family. A study assessing changing gender roles between males and females showed that as women begin to spend less time in the house, men are taking over the role of the caretaker and spending more time with children as compared to their female counterparts. Robin A. Douthitt, author of the article, "The Division of Labor Within the Home: Have Gender Roles Changed?" concluded by saying, "(1) men do not spend significantly more time with children when their wives are employed and (2) employed women spend significantly less time in child care than their full-time homemaker counterparts (3) over a 10-year period both mothers and fathers are spending more total time with children." (703).


title: Gender inequality

text: Women bear a disproportionate burden when it comes to unpaid work. In the Asia and Pacific region, women spend 4.1 times more time in unpaid work than men do. Additionally, looking at 2019 data by the OECD (Organization for Economic Co-operation and Development) countries, the average time women spent in unpaid work is 264 minutes per day compared to men who spent 136 minutes per day. Although men spend more time in paid work, women still spend more time, in general, doing both paid and unpaid work. The numbers are 482.5 minutes per day for women and 454.4 minutes per day for men. These statistics show us that there is a double burden for women.


title: Gender inequality

text: One survey showed that men rate their technological skills in activities such as basic computer functions and online participatory communication higher than women. However, this study was a self-reporting study, where men evaluate themselves on their own perceived capabilities. It thus is not data based on actual ability, but merely perceived ability, as participants' ability was not assessed. Additionally, this study is inevitably subject to the significant bias associated with self-reported data.


title: Gender inequality

text: In contrary to such findings, a carefully controlled study that analyzed data sets from 25 developing countries led to the consistent finding that the reason why fewer women access and use digital technology is a direct result of their unfavorable conditions and ongoing discrimination with respect to employment, education and income. When controlling for these variables, women turn out to be more active users of digital tools than men. This turns the alleged digital gender divide into an opportunity: given women's affinity for information and communications technology (ICT), and given that digital technologies are tools that can improve living conditions, ICT represents a concrete and tangible opportunity to tackle longstanding challenges of gender inequalities in developing countries, including access to employment, income, education and health services.


title: Gender inequality

text: Women are often drastically underrepresented within university technology and ICT focused programs while being overrepresented within social programs and humanities. Although data has shown women in western society generally outperform men in higher education, the labor markets of women often provide less opportunity and lower wages than that of men. Gender stereotypes and expectations may have an influence on the underrepresentation of women within technology and ICT focused programs and careers.Females are also underrepresented in science, technology, engineering, and mathematics (STEM) at all levels of society. Fewer females are completing STEM school subjects, graduating with STEM degrees, being employed as STEM professionals, and holding senior leadership and academic positions in STEM. The gender pay gap, family role expectations, lack of visible role models or mentors, discrimination and harassment, and bias in hiring and promotion practices exacerbate this problem.


title: Gender inequality

text: Through socialization, women may feel obligated to choose programs with characteristics that emulate gender roles and stereotypes. Studies have shown domestic expectations may also lead to less opportunities in professional progression within the technology and ICT industry. Workplace practices of technology industries often include long, demanding hours which often conflict with gendered domestic expectations. This conflict leads to less opportunity and women opting for less demanding jobs. Gendered roles and expectations may cause discriminatory tendencies during the hiring process in which employers are reluctant to hire women as a way to avoid extra costs and benefits. Tech employers reluctance to hire women result in placing them in less demanding and opportune jobs, situating female employees in lower positions that are difficult to advance in.


title: Gender inequality

text: The lack of women and the existence of gender stereotypes within the technology industry often lead to discrimination and marginalization of women by colleagues and co-workers. Women often feel as though they aren't taken seriously or feel unheard. Discrimination and gendered expectations often prevent or create difficulties for women to obtain higher positions within technology companies.


title: Gender inequality

text: Many countries have laws that give less inheritance of the ancestral property for women compared to men.


title: Gender inequality

text: Gender inequalities often stem from social structures that have institutionalized conceptions of gender differences.


title: Gender inequality

text: Marginalization occurs on an individual level when someone feels as if they are on the fringes or margins of their respective society. This is a social process and displays how current policies in place can affect people. For example, media advertisements display young girls with easy bake ovens (promoting being a housewife) as well as with dolls that they can feed and change the diaper of (promoting being a mother).


title: Gender inequality

text: Cultural stereotypes, which can dictate specific roles, are engrained in both men and women and these stereotypes are a possible explanation for gender inequality and the resulting gendered wage disparity. Women have traditionally been viewed as being caring and nurturing and are designated to occupations which require such skills. While these skills are culturally valued, they were typically associated with domesticity, so occupations requiring these same skills are not economically valued. Men have traditionally been viewed as the main worker in the home, so jobs held by men have been historically economically valued and occupations predominated by men continue to be economically valued and earn higher wages.


title: Gender inequality

text: Gender Stereotypes influenced greatly by gender expectations, different expectations on gender influence how people determine their roles, appearance, behaviors, etc. When expectations of gender roles deeply rooted in people's mind, people' values and ideas started to be influenced and leading to situation of stereotypes, which actualize their ideas into actions and perform different standards labelling the behaviors of people. Gender stereotypes limit opportunities of different gender when their performance or abilities were standardizing according to their gender-at-birth, that women and men may encounter limitations and difficulties when challenging the society through performing behaviors that their gender is "not supposed" to perform. For example, men may receive judgments when they are trying to stay at home and finish housework and support their wives to go out and work instead, as men are expected to be work outside for earning money for the family. The traditional concepts of gender stereotypes are being challenged nowadays in different societies and improvement could be observed that men could also be responsible for housework, women could also be construction worker in some societies. It is still a long process when traditional concepts and values have deep-rooted in people's mind, that higher acceptance towards gender roles and characteristics is homely to be gradually developed.


title: Gender inequality

text: Bonnie Spanier coined the term hereditary inequality. Her opinion is that some scientific publications depict human fertilization such that sperms seem to actively compete for the "passive" egg, even though in reality it is complicated (e.g. the egg has specific active membrane proteins that select sperm etc.)


title: Gender inequality

text: Gender inequality can further be understood through the mechanisms of sexism. Discrimination takes place due to the prejudiced treatment of men and women based on gender alone. Sexism occurs when men and women are framed within two dimensions of social cognition.


title: Gender inequality

text: Discrimination also plays out with networking and in preferential treatment within the economic market. Men typically occupy positions of power in society. Due to socially accepted gender roles or preference to other men, males in power are more likely to hire or promote other men, thus discriminating against women.


title: Gender inequality

text: Sonja B. Starr conducted a study in the US that found that the prison sentences that men serve are on average 63% longer than those that women serve when controlling for arrest offense and criminal history. However, the study does not purport to explain why this is the case. Starr does not believe that men are disadvantaged generally. Men's rights advocates have argued that men being over-represented in both those who commit murder and the victims of murder is evidence that men are being harmed by outmoded cultural attitudes.


title: Gender inequality

text: In a report by the Movement Advancement Project and Center for American Progress, researchers found that transgender people are overrepresented in the criminal justice system. 21% of transgender women reported that they spent time in jail compared to 5% of all U.S adults. The reason for this disproportionate rate was stated to be because transgender people are more likely to be put in vulnerable situations due to gender discrimination. Transgender people are more likely to face discrimination in the domains of housing, employment, healthcare, and identification documents, leading to higher interactions with the criminal justice system.


title: Gender inequality

text: The report also found transgender women are more likely to experience gendered violence while in prison. When transgender women were placed in men's prisons in California, 59% reported that they had been sexually assaulted compared to the 4.4% of all male-respondents. Otherwise said, Transgender women are 13 times more likely to be assaulted than incarcerated men.


title: Gender inequality

text: The New York Film Academy took a closer look at the women in Hollywood and gathered statistics from the top 500 films from 2007 to 2012, for their history and achievements, or lack of.


title: Gender inequality

text: There was a 5:1 ratio of men to women working in films. 30.8% of women having speaking characters, who may or may not have been a part of the 28.8% of women who were written to wear revealing clothing compared to the 7% of men who did, or the 26.2% of women who wore little to no clothing opposed to the 9.4% of men who did the same. A study analyzing five years of text from over 2,000 news sources found a similar 5:1 ratio of male to female names overall, and 3:1 for names in entertainment.


title: Gender inequality

text: Hollywood actresses are paid less than actors. Topping "Forbes" highest paid actors list of 2013 was Robert Downey Jr. with $75 million. Angelina Jolie topped the highest paid actresses list with $33 million, which tied with Denzel Washington ($33 million) and Liam Neeson ($32 million), who were the last two on the top ten highest paid actors list.


title: Gender inequality

text: In the 2013 Academy Awards, 140 men were nominated for an award, but only 35 women were nominated. No woman was nominated for directing, cinematography, film editing, writing (original screenplay), or original score that year. Since the Academy Awards began in 1929, only seven women producers have won the Best Picture category (all of whom were co-producers with men), and only eight women have been nominated for Best Original Screenplay. Lina Wertmuller (1976), Jane Campion (1994), Sofia Coppola (2004), and Kathryn Bigelow (2012) were the only four women to be nominated for Best Director, with Bigelow being the first woman to win for her film "The Hurt Locker". The Academy Awards' voters are 77% male.


title: Gender inequality

text: A group of Hollywood actors have launched their own social movement titled #AskMoreOfHim. This movement is built on the basis of men speaking out against sexual misconduct against females. A number of male activists, specifically in the film industry, have signed an open letter explaining their responsibility in the ownership of their actions, as well as calling out the actions of others. The letter has been signed and supported by "Friends" actor David Schwimmer, shown above, among many others. "The Hollywood Reporter" published their support saying, "We applaud the courage and pledge our support to the courageous women — and men, and gender non-conforming individuals — who have come forward to recount their experiences of harassment, abuse and violence at the hands of men in our country. As men, we have a special responsibility to prevent abuse from happening in the first place ... After all, the vast majority of sexual harassment, abuse and violence is perpetrated by men, whether in Hollywood or not." This accountability is set to change the way women are seen and treated in the film and television industry, hopefully ending in the closing of the gap women are experiencing in pay, promotion, and overall respect. This initiative was created in response to the #MeToo movement. The #MeToo movement, started by a single tweet, asked women to share their stories of sexual assault against men in a professional setting. Within one day, 30,000 women had used the hashtag sharing their stories. Many women feel as if they have more power in their voices than they ever had and are choosing to make personal claims that may have been brushed under the rug prior to the internet culture we're now living in. According to "Time" magazine, 95% of women in the film and entertainment industry report being sexually harassed by men in their industry. In addition to the #MeToo movement, women in industry are using #TimesUp, with the goal of aiming to help prevent sexual harassment in the workplace for victims who cannot afford their own resources.


title: Gender inequality

text: The media gives more weight to men in sports news: according to a study by Sports Illustrated on the news in the sports media, women's sports account for only 5.7% of the news in the media by ESPN.


title: Gender inequality

text: Another problem that has been causing increasing controversy lately is wage inequality. The fact that male athletes earn more money than females in almost all sports branches is the focus of discussion. The argument most often presented as the reason for this issue is that men's sports provide more income. However, according to the arguments that offer more realistic evaluations, women and men are not given equal opportunities in the field of sports, and women start and continue sports at a disadvantage. Some work has been done recently to prevent this inequality. According to the statements made, countries such as the USA, Spain, Sweden and Brazil announced that men and women national football team athletes will receive equal pay. It can be said that these developments are the initial steps to end gender inequality in sports.


title: Gender inequality

text: Gender inequality and discrimination are argued to cause and perpetuate poverty and vulnerability in society as a whole. Household and intra-household knowledge and resources are key influences in individuals' abilities to take advantage of external livelihood opportunities or respond appropriately to threats. High education levels and social integration significantly improve the productivity of all members of the household and improve equity throughout society. Gender Equity Indices seek to provide the tools to demonstrate this feature of poverty.


title: Gender inequality

text: Poverty has many different factors, one of which is the gender wage gap. Women are more likely to be living in poverty and the wage gap is one of the causes.


title: Gender inequality

text: There are many difficulties in creating a comprehensive response. It is argued that the Millennium Development Goals (MDGs) fail to acknowledge gender inequality as a cross-cutting issue. Gender is mentioned in MDG3 and MDG5: MDG3 measures gender parity in education, the share of women in wage employment and the proportion women in national legislatures. MDG5 focuses on maternal mortality and on universal access to reproductive health. These targets are significantly off-track.


title: Gender inequality

text: Addressing gender inequality through social protection programmes designed to increase equity would be an effective way of reducing gender inequality, according to the Overseas Development Institute (ODI). Researchers at the ODI argue for the need to develop the following in social protection in order to reduce gender inequality and increase growth:


title: Gender inequality

text: During war, combatants primarily target men. Both sexes die however, due to disease, malnutrition and incidental crime and violence, as well as the battlefield injuries which predominately affect men. A 2009 review of papers and data covering war related deaths disaggregated by gender concluded "It appears to be difficult to say whether more men or women die from conflict conditions overall." The ratio also depends on the type of war, for example in the Falklands War 904 of the 907 dead were men. Conversely figures for war deaths in 1990, almost all relating to civil war, gave ratios in the order of 1.3 males per female.


title: Gender inequality

text: Another opportunity to tackle gender inequality is presented by modern information and communication technologies. In a carefully controlled study, it has been shown that women embrace digital technology more than men. Given that digital information and communication technologies have the potential to provide access to employment, education, income, health services, participation, protection, and safety, among others (ICT4D), the natural affinity of women with these new communication tools provide women with a tangible bootstrapping opportunity to tackle social discrimination. A target of global initiatives such as the United Nations Sustainable Development Goal 5 is to enhance the use of enabling technology to promote the empowerment of women.


title: Gender inequality

text: Gender inequality is a result of the persistent discrimination of one group of people based upon gender and it manifests itself differently according to race, culture, politics, country, and economic situation. While gender discrimination happens to both men and women in individual situations, discrimination against women is more common.


title: Gender inequality

text: In the Democratic Republic of the Congo, rape and violence against women and girls is used as a tool of war. In Afghanistan, girls have had acid thrown in their faces for attending school. Considerable focus has been given to the issue of gender inequality at the international level by organizations such as the United Nations (UN), the Organisation for Economic Co-operation and Development (OECD), and the World Bank, particularly in developing countries. The causes and effects of gender inequality vary geographically, as do methods for combating it.


title: Gender inequality

text: One example of the continued existence of gender inequality in Asia is the "missing girls" phenomenon. "Many families desire male children in order to ensure an extra source of income. In China, females are perceived as less valuable for labor and unable to provide sustenance." Moreover, gender inequality is also reflected in the educational aspect of rural China. Gender inequality exists because of gender stereotypes in rural China. For example, families may consider that it is useless for girls to acquire knowledge at school because they will marry someone eventually, and their major responsibility is to take care of housework.


title: Gender inequality

text: Furthermore, the current formal education in Asia might be also a result of the historical tendencies. For instance, insufficient supply and demand for education of women reflect the development of numeracy levels throughout Asia between 1900 and 1960. Regions like South and West Asia had low numeracy levels during the early and mid-20th century. As a consequence, there were no significant gender equality trends. East Asia in its turn was characterized by a high numeracy level and gender equality. The success of this region is related to the higher education and hence higher participation rate of females in the economic life of the region.


title: Gender inequality

text: Gender inequality in China derives from deeply rooted Confucian beliefs about gender roles in society.


title: Gender inequality

text: Despite that, gender inequality in China was relatively modest before the beginning of the Chinese economic reform in 1978. The transition period to an economic system with market elements during the 1980s though was characterized by increasing gender inequality in China. On the other hand, the gender inequality was also influenced by the "One-child policy" because of the son preference. Nowadays women still face discrimination in China, despite the existence of state programs


title: Gender inequality

text: According to the United Nations Development Program, China was ranked 39 out of 162 countries on the Gender Inequality Index in 2018, while it was ranked 91 out of 187 in 2014.


title: Gender inequality

text: According to the World Economic Forum's global gender gap index, China's gap has widened and its rank has dropped to 106 out of 153 countries in 2020. It ranked last in terms of health and survival.


title: Gender inequality

text: According to Human Rights Watch, job discrimination remains a significant issue as 11% of postings specify a preference or requirement of men. In fact, Chinese women are often asked whether they expect to have children during interview as it is considered an obstacle to the job application, and as women generally retire around 40, it is difficult for them to advance.


title: Gender inequality

text: In addition, Chinese women earn 78.2% for every dollar paid to a man in 2019, according to a study conducted by Boss Zhipin.


title: Gender inequality

text: Gender inequality in South Korea is derived from deeply rooted patriarchal ideologies with specifically defined gender-roles. The gender-based stereotypes are often unchallenged and even encouraged by the government.


title: Gender inequality

text: South Korea has the lowest rank among OECD countries in the Economist's "Glass Ceiling Index", which evaluates women's higher education, number of women in managerial positions and in parliament.


title: Gender inequality

text: The gap has improved in healthcare and education, but it is still prevalent in the economy and politics. In fact, out of 36 OECD countries, South Korea ranked 30 for women's employment in 2018.


title: Gender inequality

text: Victims of gender-based discrimination struggle to make a case and get justice as it is hard to prove gender discrimination and sometimes do not complain because they are afraid of the repercussions.


title: Gender inequality

text: The existing directives against gender discrimination are not effective because the law is weakly enforced and corporations do not comply.


title: Gender inequality

text: A Cambodian said, "Men are gold, women are white cloth", emphasizing that women had a lower value and importance compared to men. In Cambodia, approximately 15% (485,000 hectares) of land was owned by women. In Asian culture, there is a stereotype that women usually have lower status than men because males carry on the family name and hold the responsibilities to take care of the family. Females have a less important role, mainly to carry out domestic chores, and taking care of husbands and children. Women are also the main victims of poverty as they have little or no access to education, low pay and low chances owning assets such as lands, homes or even basic items.


title: Gender inequality

text: In Cambodia, the Ministry of Women's Affairs (MoWA) was formed in 1998 with the role of improving women's overall power and status in the country.


title: Gender inequality

text: India ranking remains low in gender equality measures by the World Economic Forum, although the rank has been improving in recent years. When broken down into components that contribute the rank, India performs well on political empowerment, but is scored near the bottom with China on sex selective abortion. India also scores poorly on overall female to male literacy and health rankings. India with a 2013 ranking of 101 out of 136 countries had an overall score of 0.6551, while Iceland, the nation that topped the list, had an overall score of 0.8731 (no gender gap would yield a score of 1.0). Gender inequalities impact India's sex ratio, women's health over their lifetimes, their educational attainment, and economic conditions. It is a multifaceted issue that concerns men and women alike.


title: Gender inequality

text: The labor force participation rate of women was 80.7% in 2013. Nancy Lockwood of the Society for Human Resource Management, the world's largest human resources association with members in 140 countries, in a 2009 report wrote that female labor participation is lower than men, but has been rapidly increasing since the 1990s. Out of India's 397 million workers in 2001, 124 million were women, states Lockwood.


title: Gender inequality

text: India is on target to meet its Millennium Development Goal of gender parity in education before 2016. UNICEF's measures of attendance rate and Gender Equality in Education Index (GEEI) attempt to capture the quality of education. Despite some gains, India needs to triple its rate of improvement to reach GEEI score of 95% by 2015 under the Millennium Development Goals. A 1998 report stated that rural India girls continue to be less educated than the boys.


title: Gender inequality

text: Although African nations have made considerable strides towards improving gender parity, the World Economic Forum's 2018 Global Gender Gap Index reported that sub-Saharan African and North African countries have only bridged 66% and 60% of their gender inequality. Women face considerable barriers to attending equal status to men in terms of property ownership, gainful employment, political power, credit, education, and health outcomes. In addition, women are disproportionately affected by poverty and HIV/AIDs because of their lack of access to resources and cultural influences. Other key issues are adolescent births, maternal mortality, gender-based violence, child marriage, and female genital mutilation. It's estimated that 50% of adolescent childbirths and 66% of all maternal deaths occurred in sub-Saharan African nations. Women have few rights and legal protections which have led to the highest numbers of child marriage and female genital mutilation than any other continent. Furthermore, Burkina Faso, Côte d'Ivoire, Egypt, Lesotho, Mali, and Niger do not have any legal protections for gender-based domestic violence.


title: Gender inequality

text: The Global Gender Gap Report put out by the World Economic Forum (WEF) in 2013 ranks nations on a scale of 0 to 1, with a score of 1.0 indicating full gender equality. A nation with 35 women and 65 men in political office would get a score of 0.538 as the WEF is measuring the gap between the two figures and not the actual percentage of women in a given category. While Europe holds the top four spots for gender equality, with Iceland, Finland, Norway and Sweden ranking first through fourth respectively, it also contains two nations ranked in the bottom 30 countries, Albania at 108 and Turkey at 120. The Nordic Countries, for several years, have been at the forefront of bridging the gap in gender inequality. Every Nordic country, aside from Denmark which is at 0.778, has reached above a 0.800 score. In contrast to the Nordic nations, the countries of Albania and Turkey continue to struggle with gender inequality. Albania and Turkey failed to break the top 100 nations in two of four and three of four factors, respectively.


title: Gender inequality

text: Gender is also an important aspect of economic inequality. Because women continue to hold lower-paying jobs, they earn 13% less than men on average across the European Union. According to European Quality of Life Survey and European Working Conditions Survey data, women in the European Union work more hours but for less pay. Adult men (including the retired) work an average of 23 hours per week, compared to 15 hours for women.


title: Gender inequality

text: The surveys found that while men spend up to 14 hours per week doing unpaid housework and caring for children and other family members, women spend up to 28 hours per week doing the same unpaid tasks. Women work up to six hours longer than men. If all unpaid work done by men and women at the EU median wage were to be valued, it would be worth nearly €6 trillion, or 40% of European gross domestic product.


title: Gender inequality

text: Western Europe, a region most often described as comprising the non-communist members of post-WWII Europe, has, for the most part been doing well in eliminating the gender gap. Western Europe holds 12 of the top 20 spots on the Global Gender Gap Report for overall score. While remaining mostly in the top 50 nations, four Western European nations fall below that benchmark. Portugal is just outside of the top 50 at number 51 with score of 0.706 while Italy (71), Greece (81) and Malta (84) received scores of 0.689, 0.678 and 0.676, respectively.


title: Gender inequality

text: According to the United Nations, 21 EU's member states are in the top 30 in the world in terms of gender equality. However, since 2005, the European Union has slowly improved its gender equality score according to the European Institute for Gender Equality.


title: Gender inequality

text: The Council of Europe Commissioner for Human Rights has raised gender inequality as one of the main human rights problems the European countries are facing and acknowledged the slow progress in bridging gender pay gap and addressing discrimination at work.


title: Gender inequality

text: According to the European Institute for Gender Equality, the EU seems to be the closest to gender equality in the health and money domains but has a more worrying score in the domain of power. As acknowledged by the Council of Europe Commissioner for Human Rights, the EU is only slowly progressing when it comes to tackling women's underrepresentation in political decision-making.


title: Gender inequality

text: The progress towards gender equality is uneven between member states. In fact, while Sweden and Denmark appear to be the most gender-equal societies, Greece and Hungary are far from it. Italy and Cyprus are the states which improved the most.


title: Gender inequality

text: A large portion of Eastern Europe, a region most often described as the former communist members of post-WWII Europe, resides between 40th and 100th place in the Global Gender Gap Report. A few outlier countries include Lithuania, which jumped nine places (37th to 28th) from 2011 to 2013, Latvia, which has held the 12th spot for two consecutive years, Albania and Turkey.


title: Gender inequality

text: According to United Nations Development Programme, Russia's gender inequality index is 0.255, ranking it 54 out of 162 countries in 2018. Women hold 16.1% of parliamentary seats and 96.3% have reached at least a secondary level of education. Researchers calculate the loss to the annual budget due to gender segregation to be roughly 40–50%. Although women hold prominent positions in Russia's government, traditional gender roles are still prevalent, and there is room for improvement when dealing with gender pay gap, domestic violence and sexual harassment.


title: Gender inequality

text: According to the 2020 Gender Decoupling Index, which was created by the World Economic Forum with data on education, participation in the economy, political representation and health, Turkey is 130th out of 153 countries. in line. In other words, Turkey is the country with the highest gender Decoupling after 23 countries, including sharia-governed countries such as Iran, Pakistan, Saudi Arabia and undeveloped African countries such as Mali, Togo and Gambia.According to TurkStat data, 57% of women in Turkey are happy. The happiness rate of men is at the level of 47.6%.The labor force participation rate of women in Turkey refers to the place of women in working life, this rate is 36.2% in Turkey; the OECD average is 63.6%. Turkey is one of the few countries not only among the OECD countries of which it is a member, but also in the whole world, where the participation rate of women in the labor force is the lowest. Dec. According to the Human Development Report of the United Nations Development Program dated 2016, the labor force participation rate of women is 49.6% on average in the world and is significantly higher than that of Turkey.It shows that female unemployment in Turkey (14%) is higher than the OECD average (9.8%). In other words, there is a serious danger of protection for women in Turkey.The unequal position of women in working life is also reflected in economic income inequality. Women's share of gross national income is lower than that of men in all countries. But gender income inequality in Turkey is higher than the inequality seen in the OECD and world averages. Gross national income per capita for women in Turkey is 39.3% of that for men; the OECD average is 59.6%, and the world average is 55.5%.


title: Gender inequality

text: The World Economic Forum measures gender equity through a series of economic, educational, and political benchmarks. It has ranked the United States as 19th (up from 31st in 2009) in terms of achieving gender equity. The US Department of Labor has indicated that in 2009, "the median weekly earnings of women who were full-time wage and salary workers was ... 80 percent of men's". The Department of Justice found that in 2009, "the percentage of female victims (26%) of intimate partner violence was about 5 times that of male victims (5%)". As of 2019, the average number of women killed by an intimate partner each day has gone up from three to around four. The United States ranks 41st in a ranking of 184 countries on maternal deaths during pregnancy and childbirth, below all other industrialized nations and a number of developing countries, and women are just 20% of members of the United States Congress. Economically, women are significantly underrepresented in prestigious and high paying occupations like company ownership and CEO roles, where they account for just 5.5% of the latter. Women are around 15% of self-made millionaires and 11.8% of billionaires.


title: Gender inequality

text: Existing research on the topic of gender/sex and politics has found differences in political affiliation, beliefs, and voting behavior between men and women, although these differences vary across cultures. Gender is omnipresent in every culture, and while there are many factors to consider when labeling people "Democrat" or "Republican"—such as race and religion—gender is especially prominent in politics. Studying gender and political behavior poses challenges, as it can be difficult to determine if men and women actually differ in substantial ways in their political views and voting behavior, or if biases and stereotypes about gender cause people to make assumptions. However, trends in voting behavior among men and women have been proven through research.


title: Gender inequality

text: Research shows that women in postindustrial countries like the United States, Canada, and Germany primarily identified as conservative before the 1960s; however, as time has progressed and new waves of feminism have occurred, women have become more left-wing due to shared beliefs and values between women and parties more on the left. Women in these countries typically oppose war and the death penalty, favor gun control, support environment protection, and are more supportive of programs that help people of lower socioeconomic statuses. Voting behaviors of men have not experienced as drastic of a shift over the last fifty years as women in their voting behavior and political affiliations. These behaviors tend to consistently be more conservative than women overall. These trends change with every generation, and factors such as culture, race, and religion also must be considered when discussing political affiliation. These factors make the connection between gender and political affiliation complex due to intersectionality.


title: Gender inequality

text: Candidate gender also plays a role in voting behavior. Women candidates are far more likely than male candidates to be scrutinized and have their competence questioned by both men and women when they are seeking information on candidates in the beginning stages of election campaigns. Democrat male voters tend to seek more information about female Democrat candidates over male Democrat candidates. Female Republican voters tend to seek more information about female Republican candidates. For this reason, female candidates in either party typically need to work harder to prove themselves competent more than their male counterparts.


title: Gender inequality

text: Overall, politics in the United States is dominated by men, which can pose many challenges to women who decide to enter the political sphere. As the number of women participants in politics continue to increase around the world, the gender of female candidates serves as both a benefit and a hindrance within their campaign themes and advertising practices. The overarching challenge seems to be that—no matter their actions—women are unable to win in the political sphere as different standards are used to judge them when compared to their male counterparts.


title: Gender inequality

text: One area in particular that exemplifies varying perceptions between male and female candidates is the way female candidates decide to dress and how their choice is evaluated. When women decide to dress more masculine, they are perceived as being "conspicuous". When they decide to dress more feminine, they are perceived as "deficient". At the same time, however, women in politics are generally expected to adhere to the masculine standard, thereby validating the idea that gender is binary and that power is associated with masculinity. As illustrated by the points above, these simultaneous, mixed messages create a "double-bind" for women. Some scholars go on to claim that this masculine standard represents symbolic violence against women in politics.


title: Gender inequality

text: Political knowledge is a second area where male and female candidates are evaluated differently and where political science research has consistently shown women with a lower level of knowledge than their male counterparts. One reason for this finding is the argument that there are different areas of political knowledge that different groups consider. Due to this line of thought, scholars are advocating the replacement of traditional political knowledge with gender-relevant political knowledge because women are not as politically disadvantaged as it may appear.


title: Gender inequality

text: A third area that affects women's engagement in politics is their low level of political interest and perception of politics as a "men's game". Despite female candidates' political contributions being equal to that of male candidates, research has shown that women perceive more barriers to office in the form of rigorous campaigns, less overall recruitment, inability to balance office and family commitments, hesitancy to enter competitive environments, and a general lack of belief in their own merit and competence. Male candidates are evaluated most heavily on their achievements, while female candidates are evaluated on their appearance, voice, verbal dexterity, and facial features in addition to their achievements.


title: Gender inequality

text: Several forms of action have been taken to combat institutionalized sexism. People are beginning to speak up or "talk back" in a constructive way to expose gender inequality in politics, as well as gender inequality and under-representation in other institutions. Researchers who have delved into the topic of institutionalized sexism in politics have introduced the term "undoing gender". This term focuses on education and an overarching understanding of gender by encouraging "social interactions that reduce gender difference". Some feminists argue that "undoing gender" is problematic because it is context-dependent and may actually reinforce gender. For this reason, researchers suggest "doing gender differently" by dismantling gender norms and expectations in politics, but this can also depend on culture and level of government (e.g. local versus federal).


title: Gender inequality

text: Another key to combating institutionalized sexism in politics is to diffuse gender norms through "gender-balanced decision-making", particularly at the international level, which "establishes expectations about appropriate levels of women in decision-making positions." In conjunction with this solution, scholars have started placing emphasis on "the value of the individual and the importance of capturing individual experience". This is done throughout a candidate's political career—whether that candidate is male or female—instead of the collective male or female candidate experience. Five recommended areas of further study for examining the role of gender in U.S. political participation are (1) realizing the "intersection between gender and perceptions"; (2) investigating the influence of "local electoral politics"; (3) examining "gender socialization"; (4) discerning the connection "between gender and political conservatism"; and (5) recognizing the influence of female political role models in recent years. Due to the fact that gender is intricately entwined in every societal institution, gender in politics can only change once gender norms in other institutions change, as well.


title: Matrix norm

text: In mathematics, a matrix norm is a vector norm in a vector space whose elements (vectors) are matrices (of given dimensions).


title: Matrix norm

text: Given a field formula_1 of either real or complex numbers, let formula_2 be the -vector space of matrices with formula_3 rows and formula_4 columns and entries in the field formula_1. A matrix norm is a norm on formula_2.


title: Matrix norm

text: This article will always write such norms with double vertical bars (like so: formula_7). Thus, the matrix norm is a function formula_8 that must satisfy the following properties:


title: Matrix norm

text: The only feature distinguishing matrices from rearranged vectors is multiplication. Matrix norms are particularly useful if they are also sub-multiplicative:


title: Matrix norm

text: Every norm on can be rescaled to be sub-multiplicative; in some books, the terminology "matrix norm" is reserved for sub-multiplicative norms.


title: Matrix norm

text: Suppose a vector norm formula_16 on formula_17 and a vector norm formula_18 on formula_19 are given. Any formula_20 matrix induces a linear operator from formula_17 to formula_19 with respect to the standard basis, and one defines the corresponding "induced norm" or "operator norm" or "subordinate norm" on the space formula_2 of all formula_20 matrices as follows:


title: Matrix norm

text: where formula_26 denotes the supremum. This norm measures how much the mapping induced by formula_27 can stretch vectors.


title: Matrix norm

text: Depending on the vector norms formula_16, formula_18 used, notation other than formula_30 can be used for the operator norm.


title: Matrix norm

text: If the "p"-norm for vectors (formula_31) is used for both spaces formula_17 and formula_19, then the corresponding operator norm is:


title: Matrix norm

text: These induced norms are different from the "entry-wise" "p"-norms and the Schatten "p"-norms for matrices treated below, which are also usually denoted by formula_35


title: Matrix norm

text: In the special case of formula_39 (the Euclidean norm or formula_40-norm for vectors), the induced matrix norm is the "spectral norm". (The two values do "not" coincide in infinite dimensions — see Spectral radius for further discussion.) The spectral norm of a matrix formula_27 is the largest singular value of formula_27 (i.e., the square root of the largest eigenvalue of the matrix formula_43, where formula_44 denotes the conjugate transpose of formula_27):


title: Matrix norm

text: since formula_50 and similarly formula_51 by singular value decomposition (SVD). There is another important inequality:


title: Matrix norm

text: where formula_53 is the Frobenius norm. Equality holds if and only if the matrix formula_27 is a rank-one matrix or a zero matrix. This inequality can be derived from the fact that the trace of a matrix is equal to the sum of its eigenvalues.


title: Matrix norm

text: When formula_55 we have an equivalent definition for formula_56 as formula_57. It can be shown to be equivalent to the above definitions using the Cauchy–Schwarz inequality.


title: Matrix norm

text: Suppose formula_30; formula_63; and formula_64 are operator norms induced by the respective pairs of vector norms formula_65; formula_66; and formula_67. Then,


title: Matrix norm

text: for all positive integers "r", where is the spectral radius of . For symmetric or hermitian , we have equality in () for the 2-norm, since in this case the 2-norm "is" precisely the spectral radius of . For an arbitrary matrix, we may not have equality for any norm; a counterexample would be


title: Matrix norm

text: which has vanishing spectral radius. In any case, for any matrix norm, we have the spectral radius formula:


title: Matrix norm

text: A matrix norm formula_78 on formula_2 is called "consistent" with a vector norm formula_80 on formula_17 and a vector norm formula_82 on formula_19, if:


title: Matrix norm

text: for all formula_85 and all formula_86. In the special case of and formula_87, formula_78 is also called "compatible" with formula_89.


title: Matrix norm

text: All induced norms are consistent by definition. Also, any sub-multiplicative matrix norm on formula_90 induces a compatible vector norm on formula_17 by defining formula_92.


title: Matrix norm

text: These norms treat an formula_93 matrix as a vector of size formula_94, and use one of the familiar vector norms. For example, using the "p"-norm for vectors, , we get:


title: Matrix norm

text: This is a different norm from the induced "p"-norm (see above) and the Schatten "p"-norm (see below), but the notation is the same.


title: Matrix norm

text: Let formula_96 be the columns of matrix formula_27. From the original definition, the matrix formula_27 presents n data points in m-dimensional space. The formula_99 norm is the sum of the Euclidean norms of the columns of the matrix:


title: Matrix norm

text: The formula_99 norm as an error function is more robust, since the error for each data point (a column) is not squared. It is used in robust data analysis and sparse coding.


title: Matrix norm

text: When for the formula_103 norm, it is called the Frobenius norm or the Hilbert–Schmidt norm, though the latter term is used more frequently in the context of operators on (possibly infinite-dimensional) Hilbert space. This norm can be defined in various ways:


title: Matrix norm

text: where formula_107 are the singular values of formula_27. Recall that the trace function returns the sum of diagonal entries of a square matrix.


title: Matrix norm

text: The Frobenius norm is an extension of the Euclidean norm to formula_72 and comes from the Frobenius inner product on the space of all matrices.


title: Matrix norm

text: The Frobenius norm is sub-multiplicative and is very useful for numerical linear algebra. The sub-multiplicativity of Frobenius norm can be proved using Cauchy–Schwarz inequality.


title: Matrix norm

text: Frobenius norm is often easier to compute than induced norms, and has the useful property of being invariant under rotations (and unitary operations in general). That is, formula_110 for any unitary matrix formula_111. This property follows from the cyclic nature of the trace (formula_112):


title: Matrix norm

text: where formula_119 is the Frobenius inner product, and Re is the real part of a complex number (irrelevant for real matrices)


title: Matrix norm

text: Note that in some literature (such as Communication complexity), an alternative definition of max-norm, also called the formula_121-norm, refers to the factorization norm:


title: Matrix norm

text: The Schatten "p"-norms arise when applying the "p"-norm to the vector of singular values of a matrix. If the singular values of the formula_20 matrix formula_27 are denoted by "σ", then the Schatten "p"-norm is defined by


title: Matrix norm

text: These norms again share the notation with the induced and entry-wise "p"-norms, but they are different.


title: Matrix norm

text: All Schatten norms are sub-multiplicative. They are also unitarily invariant, which means that formula_126 for all matrices formula_27 and all unitary matrices formula_111 and formula_129.


title: Matrix norm

text: The most familiar cases are "p" = 1, 2, ∞. The case "p" = 2 yields the Frobenius norm, introduced before. The case "p" = ∞ yields the spectral norm, which is the operator norm induced by the vector 2-norm (see above). Finally, "p" = 1 yields the nuclear norm (also known as the "trace norm", or the Ky Fan 'n'-norm), defined as


title: Matrix norm

text: where formula_131 denotes a positive semidefinite matrix formula_132 such that formula_133. More precisely, since formula_43 is a positive semidefinite matrix, its square root is well-defined. The nuclear norm formula_135 is a convex envelope of the rank function formula_136, so it is often used in mathematical optimization to search for low rank matrices.


title: Matrix norm

text: A matrix norm formula_137 is called "monotone" if it is monotonic with respect to the Loewner order. Thus, a matrix norm is increasing if


title: Matrix norm

text: Another source of inspiration for matrix norms arises from considering a matrix as the adjacency matrix of a weighted, directed graph. The so-called "cut norm" measures how close the associated graph is to being bipartite:


title: Matrix norm

text: The cut-norm is equivalent to the induced operator norm , which is itself equivalent to the another norm, called the Grothendieck norm.


title: Matrix norm

text: To define the Grothendieck norm, first note that a linear operator is just a scalar, and thus extends to a linear operator on any . Moreover, given any choice of basis for and , any linear operator extends to a linear operator , by letting each matrix element on elements of via scalar multiplication. The Grothendieck norm is the norm of that extended operator; in symbols:


title: Matrix norm

text: for some positive numbers "r" and "s", for all matrices formula_144. In other words, all norms on formula_2 are "equivalent"; they induce the same topology on formula_2. This is true because the vector space formula_2 has the finite dimension formula_20.


title: Matrix norm

text: Moreover, for every vector norm formula_149 on formula_150, there exists a unique positive real number formula_151 such that formula_152 is a sub-multiplicative matrix norm for every formula_153.


title: Matrix norm

text: A sub-multiplicative matrix norm formula_16 is said to be "minimal", if there exists no other sub-multiplicative matrix norm formula_18 satisfying formula_156.


title: Matrix norm

text: Let formula_157 once again refer to the norm induced by the vector "p"-norm (as above in the Induced Norm section).


title: CJ McCollum

text: Christian James McCollum (born September 19, 1991) is an American professional basketball player for the New Orleans Pelicans of the National Basketball Association (NBA). During his third year in the league in 2015–16, he was named the NBA Most Improved Player.


title: CJ McCollum

text: McCollum played college basketball for the Lehigh Mountain Hawks and was named the Patriot League Player of the Year in both 2010 and 2012. He was selected by the Portland Trail Blazers with the tenth overall pick in the 2013 NBA draft. A reserve in his first two years, he became a full-time starter for the Trail Blazers in his third season after making the decision to move to shooting guard. On August 7, 2021, he was elected president of the National Basketball Players Association, replacing Chris Paul. In 2022, McCollum was traded to the New Orleans Pelicans ending his nine year run with the Blazers.


title: CJ McCollum

text: McCollum played high school basketball for the Golden Eagles at GlenOak High School in his native city of Canton, Ohio. As a freshman in 2005, he was considerably undersized, standing at only . Despite his stature, McCollum played varsity as a freshman for the Golden Eagles, relying on his athleticism. McCollum would eventually benefit from a late growth spurt, gaining five inches by his second year and another four inches by his third year of high school; it proved enough to put him on the radar for college recruitment. In his very first game as a junior, McCollum came away with 54 points to set both school and Stark County records.


title: CJ McCollum

text: Throughout his high school career, McCollum worked at refining his shooting stroke; the successful effort was reflected in the 29.3 points per game he averaged during his senior season. By graduation, McCollum had become the leading scorer in Golden Eagles history, with 1,405 career points, and was named Gatorade Ohio Player of the Year for his final campaign, the 2008–09 season.


title: CJ McCollum

text: McCollum played at the private research school Lehigh University for four seasons. Listed at and as a freshman in 2009–10, he made an immediate impact for the Mountain Hawks. He played in 33 games, starting in 31, and averaged 19.1 points and 5 rebounds per game while shooting 45.9 percent from the field. He was the leading freshman scorer in the nation and the first player in Patriot League history to be named conference Player and Rookie of the Year. Also, he was an Associated Press honorable mention All-American. McCollum led the Mountain Hawks to the 2010 NCAA tournament, where he put up 26 points in a first-round loss to a top-seeded Kansas team.


title: CJ McCollum

text: As a sophomore in 2010–11, McCollum increased his averages to 21.8 points and 7.8 rebounds per outing. He played and started in 31 contests and shot 39.9 percent from the field. His shooting percentages dipped to 39.9 percent from the field, as did Lehigh's record, and McCollum was edged out for conference Player of the Year honors by Mike Muscala of the Bucknell Bisons. McCollum was named First Team All-Conference.


title: CJ McCollum

text: As a junior in the 2011–12 campaign, McCollum again earned Patriot League Player of the Year, as well as his third straight First Team All-Conference designation. In 2012, the Mountain Hawks beat the Duke Blue Devils, 75–70, in the school's first ever victory at the NCAA Division I tournament, during which McCollum posted a game-high 30 points; this marked only the sixth time in the history of the tournament that a team seeded 15th defeated a team seeded second.


title: CJ McCollum

text: Over his four collegiate years, McCollum added 30 pounds of muscle to fill out his frame. Even though he was already considered virtually destined to be a top NBA draft pick by his third year, he decided to finish his final year of college instead of leaving sooner for the NBA. A consummate student of journalism, McCollum penned an article for "Sporting News" explaining why he opted to continue on with his education.


title: CJ McCollum

text: On November 25, 2012, McCollum scored 26 points in a 91–77 win over Sacred Heart to pass Rob Feaster as the Patriot League's all-time leading scorer. On January 5, 2013, McCollum broke his left foot in a game against Virginia Commonwealth University, ending his season early. He was a 2012–13 Senior CLASS Award finalist. McCollum went on to graduate from Lehigh University with a Bachelor of Arts in Journalism.


title: CJ McCollum

text: The first player to ever enter the NBA from Lehigh, McCollum was picked tenth overall in the 2013 NBA draft by the Portland Trail Blazers. He signed his rookie scale contract with the franchise on July 11, and he proceeded to play for them in the NBA Summer League, averaging 21 points and 4 rebounds per game.


title: CJ McCollum

text: Having convened for an annual photoshoot, the rookie class of 2013 took an NBA.com survey, according to which McCollum was voted the 2013–14 Rookie of the Year (together with Victor Oladipo). McCollum sat out the first six weeks of the regular season with a foot injury. On January 1, 2014, he was assigned to the Idaho Stampede of the development league. He was recalled by the Blazers on January 5 and made his NBA debut three days later, during which he notched 4 points as Portland beat the Orlando Magic, 110–94. On February 8, McCollum posted a season-high 19 points in a 117–110 victory over the Minnesota Timberwolves.


title: CJ McCollum

text: On October 27, 2014, Portland exercised their third-year team option to extended McCollum's rookie scale contract through 2015–16. For his sophomore season, he played 15.7 minutes per outing while averaging 6.8 points, 1.5 rebounds, and 1 assist across 62 games. During a first-round playoff loss to the Memphis Grizzlies, Game 5, McCollum scored a then career-high of 33 points.


title: CJ McCollum

text: Exercising their fourth-year team option on September 30, 2015, the Trail Blazers extended McCollum's rookie scale-contract through the 2016–17 season. With four of Portland's previous starters—LaMarcus Aldridge, Nicolas Batum, Wesley Matthews, and Robin Lopez—having departed, only star point guard Damian Lillard remained; thus McCollum was elevated to starting shooting guard to join Lillard in the backcourt for the 2015–16 campaign. As such, he saw his minutes increase to 34.8 per contest, and he started in all 80 games that he played. For the season, he would average 20.8 points, 3.2 rebounds, and 4.3 assists a night across 80 games. In the season-opener on October 28, McCollum posted a career-high 37 points, scoring 22 of which in the first quarter alone, helping the Blazers defeat the New Orleans Pelicans, 112–94. After injury decommissioned Lillard in late December, McCollum filled in as the primary point guard. On December 27, McColllum put up 35 points to go along with 11 rebounds and 9 assists during a 98–94 win over the Sacramento Kings. No Blazer had recorded numbers on par with McCollum's near triple-double in the last 29 years (Clyde Drexler posted 34 points, 11 rebounds, and 9 assists or more on five occasions.) McCollum was able to resume his starting shooting guard role on January 4 as Lillard was back on his feet, returned from injury. On February 12, he was named among the invites to All-Star Weekend's Three-Point Contest. On April 5, he posted his eighth 30-point game of the season, during a 115–107 win over Sacramento. By the end of the regular season, he averaged 20.8 points per game, while Lillard did 25.1 points, making the first backcourt to average 20 or more points apiece in Blazers' history. McCollum would subsequently earn NBA Most Improved Player honors for his breakout 2015–16 season.


title: CJ McCollum

text: McCollum helped the Blazers claim victory over the Los Angeles Clippers, 4–2, in the first round of the playoffs. However, Portland was then ousted in the second round matchup by the Golden State Warriors, going down 4–1; though it would come in the 125–121 loss that ended the Blazers' postseason run, McCollum recorded his third 27-point game of the playoffs during Game 5.


title: CJ McCollum

text: On July 27, 2016, McCollum signed a four-year contract extension with Portland. McCollum would start in all 80 games that he played and would average 23 points as well as 3.6 rebounds and as many assists. In the season-opener on October 25, he put up 25 points to help defeat the Utah Jazz, 113–104. Only four days later, he posted 23 points, 10 rebounds, 3 assists, 3 steals, and a career-high 3 blocks as Portland beat the Denver Nuggets, 115–113, in an overtime contest. During a 100–94 win over the Memphis Grizzlies on November 6, he matched his earlier career-high by racking up 37 points. On November 20, McCollum scored 33 points and hit a career-high 6 three-pointers, to defeat the Brooklyn Nets 129–109. On December 10, he set a new career-high of 7 three-pointers made and finished with 34 points scored in a 118–111 loss to the Indiana Pacers. He set another career-high for points scored with 43 on January 1 during a 95–89 win over the Timberwolves. In a game on January 13, a 115–109 loss to the Orlando Magic, he posted 26 points to extended his streak of games with 25-plus points to eight in a row, the third-longest in Blazers' history (only Geoff Petrie with 11 and Clyde Drexler with 9 games have had longer among Blazers players.) On February 7, McCollum scored 32 points; the last two of which, on a runner from the top of the lane, clinched the 114–113 win over the Dallas Mavericks with 0.9 seconds left. In a 122–113 victory over Denver on March 28, McCollum finished with a 39-point tally. The Blazers finished the regular season with a 41–41 record and entered the playoffs as the eighth seed.


title: CJ McCollum

text: On April 16, 2017, Portland lost 121–109 to the Warriors in Game 1 of the first-round series; yet McCollum's 41 points during the game was his postseason career-best and made him only the eighth Blazer with a 40-point playoff performance.


title: CJ McCollum

text: McCollum missed the opener of the 2017–18 season due to a single-game suspension incurred when he left the bench area once during a preseason game. McCollum would play in 80 games and start in all of them while averaging 21.4 points, 4 rebounds, and 3.4 assists a night. In his season debut on October 20, he put up 28 points on 12-of-18 shooting to lead his team past the Indiana Pacers, 114–96. He recorded as many as 36 points during a 98–97 loss to the Memphis Grizzlies on November 7. On the 25th of that month, McCollum had 26 points and scored 7 straight in the final quarter, as he helped Portland stage a 10–0 scoring run to overcome a 17-point deficit and defeat the Washington Wizards, 108–105. On January 1, to defeat the Chicago Bulls, 124–120, he scored 25 of 32 points after halftime, including the game-clinching basket with 56.5 seconds left in overtime. During a game on January 31, as Portland defeated the Bulls, 124–108, McCollum scored a franchise-record 28 points in the first quarter alone, and he finished with a career-high 50 points in only three periods before heading to the bench for the fourth. He joined Damian Lillard, Damon Stoudamire, Brandon Roy, Andre Miller, Clyde Drexler and Geoff Petrie as Trail Blazers to score 50 points or more. On March 28, McCollum had a 42-point effort, which came in a 108–103 loss to the Grizzlies. In Game 4 of the Trail Blazers' first-round playoff series against the New Orleans Pelicans, McCollum scored 38 points in a 131–123 loss. The loss eliminated Portland from the playoffs, the last in a four-game sweep.


title: CJ McCollum

text: Across 70 games, starting in all of them, McCollum would average 21 points, 4 rebounds, and 3 assists for the season. On November 6, 2018, McCollum scored 40 points during a 118–103 win over the Milwaukee Bucks. On December 12, he matched his season high with 40 points during a 92–83 loss to the Memphis Grizzlies. On December 23, in a game against the Warriors, McCollum moved past Damon Stoudamire (717) into fifth on the Blazers' career list for 3-pointers. On December 30, he broke out of a six-game funk by hitting 13 of 18 shots in a 35-point performance as the Trail Blazers defeated the Philadelphia 76ers 129–95. On January 22, he scored 31 points and made seven 3-pointers in a 123–114 loss to the Oklahoma City Thunder, thus passing Nicolas Batum (751) for fourth on the franchise's all-time 3-pointers list. On January 26, he recorded his first career triple-double with 28 points, 10 assists, and 10 rebounds in a 120–111 win over the Atlanta Hawks. On March 1, he scored 35 points and matched a career best by making seven 3-pointers in a 119–117 loss to the Toronto Raptors. McCollum missed 10 games over late March and early April with a left knee injury. In Game 3 of the Trail Blazers' second-round playoff series against the Denver Nuggets, McCollum matched his career playoff high with 41 points during a 140–137 win in quadruple-overtime. In Game 6, he scored 30 points in a 119–108 win, helping the Blazers tie the series against the Nuggets at 3–3. In the deciding Game 7, he scored a game-high 37 points in a 100–96 win, including the game-sealing step back jumper with 15 seconds remaining, to help the Blazers advance to the Western Conference Finals for the first time since 2000. Portland went on to lose the Conference Finals in a four-game sweep to the Warriors.


title: CJ McCollum

text: On November 21, 2019, McCollum scored a then season-high 37 points, along with 6 rebounds and 10 assists, in a 137–129 loss to the Milwaukee Bucks. On February 23, 2020, he would surpass that season-high with a 41-point, 9-rebound, 12-assist performance in a 107–104 victory over the Detroit Pistons. McCollum matched his season-high on March 2, scoring 41 points in a 130–107 win over the Orlando Magic.


title: CJ McCollum

text: On December 26, 2020, McCollum scored a season-high 44 points, along with a game-winning three-pointer, in a 128–126 overtime win against the Houston Rockets. On August 7, 2021, McCollum was elected president of the National Basketball Players Association, succeeding Chris Paul who had served since 2013.


title: CJ McCollum

text: On December 7, 2021, McCollum was diagnosed with a pneumothorax and was ruled out indefinitely. On January 17, 2022, he made his return from the injury, logging 16 points in a 98–88 win over the Orlando Magic.


title: CJ McCollum

text: On February 8, 2022, Portland traded McCollum, Larry Nance Jr. and Tony Snell to the New Orleans Pelicans in exchange for Josh Hart, Nickeil Alexander-Walker, Tomáš Satoranský, Didi Louzada, a protected 2022 first-round draft pick, the better of New Orleans' and Portland's 2026 second-round draft picks and New Orleans' 2027 second-round draft pick. Two days later, McCollum made his Pelicans debut, putting up 15 points, seven rebounds, and five assists in a 112–97 loss to the Miami Heat. On April 13 during the NBA Play-in Tournament, McCollum recorded 32 points, 6 rebounds, and 7 assists leading the Pelicans past the San Antonio Spurs 113–103 and advancing New Orleans to the eight seed game.


title: CJ McCollum

text: McCollum hosts a weekly podcast, "Pull Up with CJ McCollum", that is produced by Cadence13. It is co-hosted by ESPN analyst Jordan Schultz. McCollum has a podcast studio in his home and brings portable recording equipment with him when he is out of town. Guests on the show have included Kevin Durant and Carmelo Anthony. In a March 2020 episode of the podcast, McCollum was recording when he received news that the NBA was suspending the 2020 season due to the COVID-19 pandemic.


title: CJ McCollum

text: McCollum has been married to his college sweetheart Elise Esposito since October 27, 2020. They have one son named Jacobi who was born on January 10, 2022. McCollum's older brother, Errick, is also a professional basketball player. Off the court, McCollum has long taken a keen interest in journalism. As such, he has written articles concerning the NBA for various media outlets; in one of his pieces, he interviewed the Commissioner of the league Adam Silver.


title: CJ McCollum

text: McCollum is involved in his community as a radio personality and philanthropist. In 2016, he opened up the CJ McCollum Dream Center, which is an innovative learning room at the Blazers Boys & Girls Club outfitted with new computers, books, art, and learning tools. The Center aims to provide a safe and inspiring space for underserved youth to learn, explore, create, and grow. McCollum also helps foster local youths' interest in journalists through an initiative called CJ's Press Pass; it grants aspiring journalists access to postgame news conferences and provides them the opportunity to attend events with McCollum, to receive personalized mentorship from members of the media, and to have their work published.


title: CJ McCollum

text: McCollum is a wine enthusiast. During the NBA coronavirus bubble, he brought 84 bottles in with him and kept his hotel room temperature at or below to protect it. He has his own label, McCollum Heritage 91, named after the street he grew up on and his birth year.


title: Lydia

text: Lydia (Lydian: 𐤮𐤱𐤠𐤭𐤣𐤠, "Śfarda"; Aramaic: "Lydia"; , "Lȳdíā"; ) was an Iron Age kingdom of western Asia Minor located generally east of ancient Ionia in the modern western Turkish provinces of Uşak, Manisa and inland Izmir. The ethnic group inhabiting this kingdom are known as the Lydians, and their language, known as Lydian, was a member of the Anatolian branch of the Indo-European language family. The capital of Lydia was Sardis.


title: Lydia

text: The Kingdom of Lydia existed from about 1200 BC to 546 BC. At its greatest extent, during the 7th century BC, it covered all of western Anatolia. In 546 BC, it became a province of the Achaemenid Persian Empire, known as the satrapy of Lydia or "Sparda" in Old Persian. In 133 BC, it became part of the Roman province of Asia.


title: Lydia

text: The endonym "Śfard" (the name the Lydians called themselves) survives in bilingual and trilingual stone-carved notices of the Achaemenid Empire: the satrapy of "Sparda" (Old Persian), "Saparda", Babylonian "Sapardu", Elamitic "Išbarda", Hebrew . These in the Greek tradition are associated with Sardis, the capital city of King Gyges, constructed during the 7th century BC. Lydia is called "Kisitan" by Hayton of Corycus (in "The Flower of the History of the East"), a name which was corrupted to "Quesiton" in "The Travels of Sir John Mandeville".


title: Lydia

text: The region of the Lydian kingdom was during the 15th–14th centuries BCE part of the Arzawa kingdom. However, the Lydian language is usually not categorized as part of the Luwic subgroup, unlike the other nearby Anatolian languages Luwian, Carian, and Lycian.


title: Lydia

text: The boundaries of historical Lydia varied across the centuries. It was bounded first by Mysia, Caria, Phrygia and coastal Ionia. Later, the military power of Alyattes and Croesus expanded Lydia, which, with its capital at Sardis, controlled all Asia Minor west of the River Halys, except Lycia. After the Persian conquest the River Maeander was regarded as its southern boundary, and during imperial Roman times Lydia comprised the country between Mysia and Caria on the one side and Phrygia and the Aegean Sea on the other.


title: Lydia

text: The Lydian language was an Indo-European language in the Anatolian language family, related to Luwian and Hittite. Due to its fragmentary attestation, the meanings of many words are unknown but much of the grammar has been determined. Similar to other Anatolian languages, it featured extensive use of prefixes and grammatical particles to chain clauses together. Lydian had also undergone extensive syncope, leading to numerous consonant clusters atypical of Indo-European languages. Lydian finally became extinct during the 1st century BC.


title: Lydia

text: Lydia developed after the decline of the Hittite Empire in the 12th century BC. In Hittite times, the name for the region had been Arzawa. According to Greek source, the original name of the Lydian kingdom was "Maionia" (Μαιονία), or "Maeonia": Homer ("Iliad" ii. 865; v. 43, xi. 431) refers to the inhabitants of Lydia as "Maiones" (Μαίονες). Homer describes their capital not as Sardis but as "Hyde" ("Iliad" xx. 385); Hyde may have been the name of the district in which Sardis was located. Later, Herodotus ("Histories" i. 7) adds that the "Meiones" were renamed Lydians after their king Lydus (Λυδός), son of Atys, during the mythical epoch that preceded the Heracleid dynasty. This etiological eponym served to account for the Greek ethnic name "Lydoi" (Λυδοί). The Hebrew term for Lydians, "Lûḏîm" (לודים), as found in the Book of Jeremiah (46.9), has been similarly considered, beginning with Flavius Josephus, to be derived from Lud son of Shem; however, Hippolytus of Rome (234 AD) offered an alternative opinion that the Lydians were descended from Ludim, son of Mizraim. During Biblical times, the Lydian warriors were famous archers. Some Maeones still existed during historical times in the upland interior along the River Hermus, where a town named Maeonia existed, according to Pliny the Elder ("Natural History" book v:30) and Hierocles (author of Synecdemus).


title: Lydia

text: Lydian mythology is virtually unknown, and their literature and rituals have been lost due to the absence of any monuments or archaeological finds with extensive inscriptions; therefore, myths involving Lydia are mainly from Greek mythology.


title: Lydia

text: For the Greeks, Tantalus was a primordial ruler of mythic Lydia, and Niobe his proud daughter; her husband Amphion associated Lydia with Thebes in Greece, and through Pelops the line of Tantalus was part of the founding myths of Mycenae's second dynasty. (In reference to the myth of Bellerophon, Karl Kerenyi remarked, in "The Heroes of The Greeks" 1959, p. 83. "As Lykia was thus connected with Crete, and as the person of Pelops, the hero of Olympia, connected Lydia with the Peloponnesos, so Bellerophontes connected another Asian country, or rather two, Lykia and Karia, with the kingdom of Argos".)


title: Lydia

text: In Greek myth, Lydia had also adopted the double-axe symbol, that also appears in the Mycenaean civilization, the "labrys". Omphale, daughter of the river Iardanos, was a ruler of Lydia, whom Heracles was required to serve for a time. His adventures in Lydia are the adventures of a Greek hero in a peripheral and foreign land: during his stay, Heracles enslaved the Itones; killed Syleus, who forced passers-by to hoe his vineyard; slew the serpent of the river Sangarios (which appears in the heavens as the constellation Ophiucus) and captured the simian tricksters, the Cercopes. Accounts tell of at least one son of Heracles who was born to either Omphale or a slave-girl: Herodotus ("Histories" i. 7) says this was Alcaeus who began the line of Lydian Heracleidae which ended with the death of Candaules c. 687 BC. Diodorus Siculus (4.31.8) and Ovid ("Heroides" 9.54) mentions a son called Lamos, while pseudo-Apollodorus ("Bibliotheke" 2.7.8) gives the name Agelaus and Pausanias (2.21.3) names Tyrsenus as the son of Heracles by "the Lydian woman". All three heroic ancestors indicate a Lydian dynasty claiming Heracles as their ancestor. Herodotus (1.7) refers to a Heraclid dynasty of kings who ruled Lydia, yet were perhaps not descended from Omphale. He also mentions (1.94) the legend that the Etruscan civilization was founded by colonists from Lydia led by Tyrrhenus, brother of Lydus. Dionysius of Halicarnassus was skeptical of this story, indicating that the Etruscan language and customs were known to be totally dissimilar to those of the Lydians. In addition, the story of the "Lydian" origins of the Etruscans was not known to Xanthus of Lydia, an authority on the history of the Lydians.


title: Lydia

text: Later chronologists ignored Herodotus' statement that Agron was the first Heraclid to be a king, and included his immediate forefathers Alcaeus, Belus, and Ninus in their list of kings of Lydia. Strabo (5.2.2) has Atys, father of Lydus and Tyrrhenus, as a descendant of Heracles and Omphale but that contradicts virtually all other accounts which name Atys, Lydus, and Tyrrhenus among the pre-Heraclid kings and princes of Lydia. The gold deposits in the river Pactolus that were the source of the proverbial wealth of Croesus (Lydia's last king) were said to have been left there when the legendary king Midas of Phrygia washed away the "Midas touch" in its waters.


title: Lydia

text: In Euripides' tragedy "The Bacchae", Dionysus, while maintaining his human disguise, declares his country to be Lydia.