On the conjugate product of complex polynomial matrices

Authors:
Ai-Guo Wu;Wanquan Liu;Guang-Ren Duan
Affiliations:
Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518055, PR China;Department of Computing, Curtin University, Perth, WA 6102, Australia;Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, PR China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2011

Citing 6
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Abstract

In this paper, we propose a new operator of conjugate product for complex polynomial matrices. Elementary transformations are first investigated for the conjugate product. It is shown that an arbitrary complex polynomial matrix can be converted into the so-called Smith normal form by elementary transformations in the framework of conjugate product. Then the concepts of greatest common divisors and coprimeness are proposed and investigated, and some necessary and sufficient conditions for the coprimeness are established. Finally, it is revealed that two complex matrices A and B are consimilar if and only if (sI-A) and (sI-B) are conequivalent. Such a fact implies that the Jordan form of a complex matrix A under consimilarity may be obtained by analyzing the Smith normal form of (sI-A).