motivating diagonalization of a matrix I have to teach about diagonalization of a matrix to a first year undergrad student and I was wondering what would be a good way to motivate this concept. I would appreciate any suggestions. Thanks!
Why do we need a diagonal matrix? Apart from simplifying matrix powers, why do want to diagonalize a matrix? Do they have any appealing application which can be used to motivate to study diagonal matrices.  Thanks for any answers.
What are recommended, general strategies to start block-cipher design and/or analysis? I (and many others for that matter) have always been fascinated by the inner workings of the modern building block of cryptography: block ciphers.  Now, the ressources on the "black art" of design and analysis of these ciphers are sparse; especially for the entry level. Available information like  seems to be somewhat outdated (due to its age).  What's the general consensus of the “best” (read: recommended) strategy to start designing and/or analyzing modern cryptographical block ciphers?    Nota bene: Think of this as a general, wiki-alike question – for learning purposes only. (Besides that, this Q&amp;A would represent a place we can point people to when alike algorithm design questions arise.)