The complete solution to the Sylvester-polynomial-conjugate matrix equations
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 cla...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Pergamon
2011
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/26519 |
| _version_ | 1848752009789833216 |
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| author | Wu, A. Feng, G. Liu, Wan-Quan Duan, G. |
| author_facet | Wu, A. Feng, G. Liu, Wan-Quan Duan, G. |
| author_sort | Wu, A. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T08:01:49Z |
| format | Journal Article |
| id | curtin-20.500.11937-26519 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:01:49Z |
| publishDate | 2011 |
| publisher | Pergamon |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-265192017-09-13T16:07:58Z The complete solution to the Sylvester-polynomial-conjugate matrix equations Wu, A. Feng, G. Liu, Wan-Quan Duan, G. Sylvester-polynomial-conjugate matrix equations Sylvester-conjugate sum Complete solution Conjugate product 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. 2011 Journal Article http://hdl.handle.net/20.500.11937/26519 10.1016/j.mcm.2010.12.038 Pergamon unknown |
| spellingShingle | Sylvester-polynomial-conjugate matrix equations Sylvester-conjugate sum Complete solution Conjugate product Wu, A. Feng, G. Liu, Wan-Quan Duan, G. The complete solution to the Sylvester-polynomial-conjugate matrix equations |
| title | The complete solution to the Sylvester-polynomial-conjugate matrix equations |
| title_full | The complete solution to the Sylvester-polynomial-conjugate matrix equations |
| title_fullStr | The complete solution to the Sylvester-polynomial-conjugate matrix equations |
| title_full_unstemmed | The complete solution to the Sylvester-polynomial-conjugate matrix equations |
| title_short | The complete solution to the Sylvester-polynomial-conjugate matrix equations |
| title_sort | complete solution to the sylvester-polynomial-conjugate matrix equations |
| topic | Sylvester-polynomial-conjugate matrix equations Sylvester-conjugate sum Complete solution Conjugate product |
| url | http://hdl.handle.net/20.500.11937/26519 |