Let us assume we have a square matrix $A$ whose entries are sampled from a standard Gaussian distribution of mean $0$. Do we have any information about the distribution of its eigenvalues?
Particularly, I'm aware that there are different results on symmetric gaussian matrices (or, the Gaussian orthogonal ensemble of $A$):
- The eigenvalues follow a semicircle law
Is there an equivalent result for standard, non-symmetric Gaussian matrices?