The complete solution to the Sylvester-polynomial-conjugate matrix equations

Ai-Guo Wu; Gang Feng; Wanquan Liu; Guang-Ren Duan

doi:10.1016/j.mcm.2010.12.038

Author(s)

Ai-Guo Wu
Gang Feng
Wanquan Liu
Guang-Ren Duan

Detail(s)

Original language	English
Pages (from-to)	2044-2056
Journal / Publication	Mathematical and Computer Modelling
Volume	53
Issue number	9-10
Publication status	Published - May 2011

Link(s)

DOI	DOI https://doi.org/10.1016/j.mcm.2010.12.038 Final Published version
	Check@CityULib
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-79551475867&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(60adc3f0-1133-4687-857a-2cb163746a84).html

Abstract

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. © 2010 Elsevier Ltd.

Research Area(s)

Complete solution, Conjugate product, Sylvester-conjugate sum, Sylvester-polynomial-conjugate matrix equations

Citation Format(s)

[ RIS ] [ BibTeX ]

The complete solution to the Sylvester-polynomial-conjugate matrix equations. / Wu, Ai-Guo; Feng, Gang; Liu, Wanquan; Duan, Guang-Ren.

In: Mathematical and Computer Modelling, Vol. 53, No. 9-10, 05.2011, p. 2044-2056.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review

Wu, A-G, Feng, G, Liu, W & Duan, G-R 2011, 'The complete solution to the Sylvester-polynomial-conjugate matrix equations', Mathematical and Computer Modelling, vol. 53, no. 9-10, pp. 2044-2056. https://doi.org/10.1016/j.mcm.2010.12.038

Wu, A-G., Feng, G., Liu, W., & Duan, G-R. (2011). The complete solution to the Sylvester-polynomial-conjugate matrix equations. Mathematical and Computer Modelling, 53(9-10), 2044-2056. https://doi.org/10.1016/j.mcm.2010.12.038

Wu A-G, Feng G, Liu W, Duan G-R. The complete solution to the Sylvester-polynomial-conjugate matrix equations. Mathematical and Computer Modelling. 2011 May;53(9-10):2044-2056. https://doi.org/10.1016/j.mcm.2010.12.038

Wu, Ai-Guo ; Feng, Gang ; Liu, Wanquan ; Duan, Guang-Ren. / The complete solution to the Sylvester-polynomial-conjugate matrix equations. In: Mathematical and Computer Modelling. 2011 ; Vol. 53, No. 9-10. pp. 2044-2056.