On the Hermitian R-Conjugate Solution of a System of Matrix Equations
Let R be an n by n nontrivial real symmetric involution matrix, that is, R=R−1=RT≠In. An n×n complex matrix A is termed R-conjugate if A¯=RAR, where A¯ denotes the conjugate of A. We give necessary and sufficient conditions for the existence of the Hermitian R-conjugate solution to the system of com...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/398085 |
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| _version_ | 1832567290663534592 |
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| author | Chang-Zhou Dong Qing-Wen Wang Yu-Ping Zhang |
| author_facet | Chang-Zhou Dong Qing-Wen Wang Yu-Ping Zhang |
| author_sort | Chang-Zhou Dong |
| collection | DOAJ |
| description | Let R be an n by n nontrivial real symmetric involution matrix, that is,
R=R−1=RT≠In. An n×n complex matrix A is termed R-conjugate if
A¯=RAR, where A¯ denotes the conjugate of A. We give necessary and sufficient
conditions for the existence of the Hermitian R-conjugate solution to the system
of complex matrix equations AX=C and XB=D and present an expression of
the Hermitian R-conjugate solution to this system when the solvability conditions
are satisfied. In addition, the solution to an optimal approximation problem is
obtained. Furthermore, the least squares Hermitian R-conjugate solution with the
least norm to this system mentioned above is considered. The representation of
such solution is also derived. Finally, an algorithm and numerical examples are
given. |
| format | Article |
| id | doaj-art-1f3949f28fc644f9a73fb4da74fe5324 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-1f3949f28fc644f9a73fb4da74fe53242025-02-03T01:01:48ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/398085398085On the Hermitian R-Conjugate Solution of a System of Matrix EquationsChang-Zhou Dong0Qing-Wen Wang1Yu-Ping Zhang2School of Mathematics and Science, Shijiazhuang University of Economics, Shijiazhuang, Hebei 050031, ChinaDepartment of Mathematics, Shanghai University, Shanghai, Shanghai 200444, ChinaDepartment of Mathematics, Ordnance Engineering College, Shijiazhuang, Hebei 050003, ChinaLet R be an n by n nontrivial real symmetric involution matrix, that is, R=R−1=RT≠In. An n×n complex matrix A is termed R-conjugate if A¯=RAR, where A¯ denotes the conjugate of A. We give necessary and sufficient conditions for the existence of the Hermitian R-conjugate solution to the system of complex matrix equations AX=C and XB=D and present an expression of the Hermitian R-conjugate solution to this system when the solvability conditions are satisfied. In addition, the solution to an optimal approximation problem is obtained. Furthermore, the least squares Hermitian R-conjugate solution with the least norm to this system mentioned above is considered. The representation of such solution is also derived. Finally, an algorithm and numerical examples are given.http://dx.doi.org/10.1155/2012/398085 |
| spellingShingle | Chang-Zhou Dong Qing-Wen Wang Yu-Ping Zhang On the Hermitian R-Conjugate Solution of a System of Matrix Equations Journal of Applied Mathematics |
| title | On the Hermitian R-Conjugate Solution of a System of Matrix Equations |
| title_full | On the Hermitian R-Conjugate Solution of a System of Matrix Equations |
| title_fullStr | On the Hermitian R-Conjugate Solution of a System of Matrix Equations |
| title_full_unstemmed | On the Hermitian R-Conjugate Solution of a System of Matrix Equations |
| title_short | On the Hermitian R-Conjugate Solution of a System of Matrix Equations |
| title_sort | on the hermitian r conjugate solution of a system of matrix equations |
| url | http://dx.doi.org/10.1155/2012/398085 |
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