Copyright © 2013 Huamin Zhang and Feng Ding. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper studies the properties of the Kronecker product related to the mixed matrix products, the vector operator, and the vec-permutation matrix and gives several theorems and their proofs. In addition, we establish the relations between the singular values of two matrices and their Kronecker product and the relations between the determinant, the trace, the rank, and the polynomial matrix of the Kronecker products.