given A and B are mxn and nxm matrices. What can we say about their eigenvalues

Question

I know that the sum of the eigenvalues will be the same. But can we say something about them individually? When A is transpose(B) I'm getting something interesting

A = (1 2 0) (0 -1 2)

B = (1 0) (2 -1) (0 2)

AB has 7,3 as eigenvalues BA has 3,7,0 as eigenvalues

Answer 1

Eigenvalues aren't defined for rectangular matrices, but the singular values are closely related: The right and left singular values for rectangular matrix $M$ are the eigenvalues of $M'M$ and $MM'.$

Source: Eigenvalues of a rectangular matrix