Let $\mathbf{A}\in\mathbb{R}^{m\times n}$ and $\mathbf{B}\in\mathbb{R}^{n\times m}$ be rectangular matrices. What can we say about the eigenvalues of their Kronecker product $\mathbf{A} \otimes \mathbf{B}$???
One observes that $A$ and $B$ are not square matrices, so we can not talk about their eigenvalues. However, the Kronecker product defines a square matrix and has a set of $nm-$eigenvalues.
I am not asking about the trivial eigenvalues due to the rank deficiency of the matrix $\mathbf{A} \otimes \mathbf{B}$.