The complete solution to the Sylvester-polynomial-conjugate matrix equations
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Wu, Ai-Guo and Feng, Gang and Liu, Wanquan and Duan, Guang-Ren. 2011. The complete solution to the Sylvester-polynomial-conjugate matrix equations. Mathematical and Computer Modelling. 53: pp. 2044-2056.
Mathematical and Computer Modelling
Department of Computing
In this paper we propose two new operators for complex polynomial matrices. One is the conjugate product and the other is the Sylvester-conjugate sum. Then some important properties for these operators are proved. Based on these derived results, we propose a unified approach to solving a general class of Sylvester-polynomial-conjugate matrix equations, which include the Yakubovich-conjugate matrix equation as a special case. The complete solution of the Sylvester-polynomial-conjugate matrix equation is obtained in terms of the Sylvester-conjugate sum, and such a proposed solution can provide all the degrees of freedom with an arbitrarily chosen parameter matrix.
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