Things Fourier

For some reason several classes at MIT this year involve Fourier analysis. I was always confused about this as a high schooler, because no one ever gave me the ``orthonormal basis'' explanation, so here goes. As a bonus, I also prove a form of Arrow's Impossibility Theorem using binary Fourier analysis, and then talk about… Continue reading Things Fourier

Rant: Matrices Are Not Arrays of Numbers

The following is an excerpt from a current work of mine. I thought I'd share it here, as some people have told me they enjoyed it. As I'll stress repeatedly, a matrix represents a linear map between two vector spaces. Writing it in the form of an $latex {m \times n}&fg=000000$ matrix is merely a… Continue reading Rant: Matrices Are Not Arrays of Numbers