When will eigenvalues of a matrix be positive? This may be very general question, Are there any set of conditions that if some arbitrary matrix say A fulfils we can say that A will have eigenvalues such that all of them are non negative. In other words what are conditions for a matrix to be positive semi definite.
Regards
Ahsan 

Start with the equation $Ax = ax$ for eigenvalue $a$ and eigenvector $x$ of a matrix $A$. Then multiply by the left with $x^T$. Other hint: $x^T x > 0$.
