[math-fun] Elementary (?) matrix question

I hate to be so dense about linear algebra, but here's another matrix question: Given an _arbitrary_ square matrix M with complex entries, we can compute the matrix product M.M', where M' is the conjugate transpose of M. Clearly, M.M' is Hermitian, so all of its eigenvalues are real. Question: Is there any interesting relationship between the eigenvalues of M.M' and those of M ? There's an obvious one from the fact det(M.M')=det(M)det(M'). Also, trace(M.M') is the sum of the squares of the absolute values of the entries of M.