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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 296185, 8 pages
http://dx.doi.org/10.1155/2013/296185
Research Article

On the Kronecker Products and Their Applications

1Key Laboratory of Advanced Process Control for Light Industry of Ministry of Education, Jiangnan University, Wuxi 214122, China
2Department of Mathematics and Physics, Bengbu College, Bengbu 233030, China

Received 10 March 2013; Accepted 6 June 2013

Academic Editor: Song Cen

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.