Eigenvalues of random matrices

Recently, Twitter introduced me to the Circular Law, which is extremely cool. Not only do the (complex) eigenvalues of a random matrix end up distributed inside a circle, they do so quite uniformly due to a "repulsion" effect.

I wondered a little bit about what this repulsion looks like, and wrote some code to visualise it - https://github.com/simon-frankau/eigenvalues. I won't bother with an image here, you can click through to see what it looks like, but I found it a fun little project to do some basic numerical stuff. The "nalgebra" and "plotters" crates were a pleasant surprise.

Posted 2021-07-18.