Fill an *n×n* matrix with independent and identically distributed values with variance *n* and mean *0*.

Now plot the eigenvalues in the complex plane. As *n → ∞*, the eigenvalues become uniformly distributed in the complex unit disc!

For small *n*, there is a concentration along the real line, but this disappears as *n → ∞*.
For this visualisation I've used 100 iterations of *n = 50*.

- Inspired by Favorite Eigenvalue Problems, SIAM News, Volume 44, Number 10, December 2011.
- Girko's Circular Law on MathWorld.
- Random matrices: the circular law: summary of a paper by Terence Tao and Van Vu, which generalises the circular law.

© Jason Davies 2012.