Circular law states the eigenvalues of a matrix with random entries of mean 0 and variance 1/n are approximately uniformly distributed in the unit disk of the complex plane. To see this, create a random matrix:
n = 1000 x = randomu(seed, n, n) - 0.5 x *= sqrt(12.0 / n)
Find the eigenvalues:
eigenvalues = la_eigenproblem(x, eigenvectors=eigenvectors)
plot, real_part(eigenvalues), imaginary(eigenvalues), $ psym=3, $ xstyle=1, xrange=[-1.5, 1.5], $ ystyle=1, yrange=[-1.5, 1.5]
This gives a plot like below:
Via the excellent John D. Cook blog. I recommend reading his site if you are interested in a combination of mathematics and Python.