On the number of invariant factors of matrix products - Sá, E. Marques de (2005)
We prove an inequality relating the number of nontrivial invariant factors of n × n matrices A and B, with those of AB, and get some results on the cases of equality. In particular, we characterize the similarity classes, and , with all eigenvalues in the base field, such that AB is nilpotent for some and .