I'm Alive

I'm alive! This has been a very difficult week in the math homework department. I'll post updates later as well as the statement (and maybe proof) of the linear analysis exercise that kicked my bum this time around.

This week reminds me of a time where a friend of mine said that my course list of linear analysis, network optimization, and numerical analysis sounds like an "undergraduate-level" curriculum. I find this very amusing. My classmates might not agree.

Speaking of numerical analysis, for now I'll share a cool picture. The series of plots below comes from the following problem: in a 15x40 matrix of zeros, insert ones into the appropriate places such that the word "HELLO" is spelled out diagonally across the matrix. Given the construction, prove that the matrix has rank 10, computationally verify, and then calculate optimal rank 1 to rank 9 approximations of the matrix and plot the approximations.

So these are the rank 1 to rank 10 approximations, then. Pretty, huh? You can find the precise problem statement here on Page 68, Exercise 9.3. It's a nice problem if you want to learn how to use matplotlib's plotting techniques!