On the number of invariant factors of matrix products - Sá, E. Marques de (2005)
In the first part of the paper we determine bounds for the ranks of certain submatrices of square matrices taken from a prescribed similarity class. Then we discuss the concept of offdiagonal indices (defined in Section 1) which, very roughly speaking, measure, for each given integer s, how far we have to go off the main diagonal of a square matrix, to find an s s nonzero minor. Some open problems are stated.