Constrained Solutions of a System of Matrix Equations
We derive the necessary and sufficient conditions of and the expressions for the orthogonal solutions, the symmetric orthogonal solutions, and the skew-symmetric orthogonal solutions of the system of matrix equations AX=B and XC=D, respectively. When the matrix equations are not consistent, the leas...
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| Main Authors: | , |
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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/10.1155/2012/471573 |
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| _version_ | 1832562941110517760 |
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| author | Qing-Wen Wang Juan Yu |
| author_facet | Qing-Wen Wang Juan Yu |
| author_sort | Qing-Wen Wang |
| collection | DOAJ |
| description | We derive the necessary and sufficient conditions of and the expressions for the orthogonal solutions, the symmetric orthogonal solutions, and the skew-symmetric orthogonal solutions of the system of matrix equations AX=B and XC=D, respectively. When the matrix equations are not consistent, the least squares symmetric orthogonal solutions and the least squares skew-symmetric orthogonal solutions are respectively given. As an auxiliary, an algorithm is provided to compute the least squares symmetric orthogonal solutions, and meanwhile an example is presented to show that it is reasonable. |
| format | Article |
| id | doaj-art-42a9c4f7264e4c379321bc265f23d649 |
| 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-42a9c4f7264e4c379321bc265f23d6492025-02-03T01:21:18ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/471573471573Constrained Solutions of a System of Matrix EquationsQing-Wen Wang0Juan Yu1Department of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, 99 Shangda Road, Shanghai 200444, ChinaWe derive the necessary and sufficient conditions of and the expressions for the orthogonal solutions, the symmetric orthogonal solutions, and the skew-symmetric orthogonal solutions of the system of matrix equations AX=B and XC=D, respectively. When the matrix equations are not consistent, the least squares symmetric orthogonal solutions and the least squares skew-symmetric orthogonal solutions are respectively given. As an auxiliary, an algorithm is provided to compute the least squares symmetric orthogonal solutions, and meanwhile an example is presented to show that it is reasonable.http://dx.doi.org/10.1155/2012/471573 |
| spellingShingle | Qing-Wen Wang Juan Yu Constrained Solutions of a System of Matrix Equations Journal of Applied Mathematics |
| title | Constrained Solutions of a System of Matrix Equations |
| title_full | Constrained Solutions of a System of Matrix Equations |
| title_fullStr | Constrained Solutions of a System of Matrix Equations |
| title_full_unstemmed | Constrained Solutions of a System of Matrix Equations |
| title_short | Constrained Solutions of a System of Matrix Equations |
| title_sort | constrained solutions of a system of matrix equations |
| url | http://dx.doi.org/10.1155/2012/471573 |
| work_keys_str_mv | AT qingwenwang constrainedsolutionsofasystemofmatrixequations AT juanyu constrainedsolutionsofasystemofmatrixequations |