A simple method for solving matrix equations $ AXB = D $ and $ GXH = C $
A simple method to solve the common solution to the pair of linear matrix equations $ AXB = D $ and $ GXH = C $ is introduced. Some necessary and sufficient conditions for the existence of a common solution, and two expressions for the general common solution of the equation pair are provided by the...
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | http://awstest.aimspress.com/article/doi/10.3934/math.2021156?viewType=HTML |
| _version_ | 1831685346182561792 |
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| author | Huiting Zhang Hairui Zhang Lina Liu Yongxin Yuan |
| author_facet | Huiting Zhang Hairui Zhang Lina Liu Yongxin Yuan |
| author_sort | Huiting Zhang |
| collection | DOAJ |
| description | A simple method to solve the common solution to the pair of linear matrix equations $ AXB = D $ and $ GXH = C $ is introduced. Some necessary and sufficient conditions for the existence of a common solution, and two expressions for the general common solution of the equation pair are provided by the proposed method. Subsequently, the results are applied to determine the solution of the matrix equation $ AXB+GYH = D $ and the Hermitian solution of the matrix equation $ AXB = D. $ |
| first_indexed | 2024-12-20T08:18:59Z |
| format | Article |
| id | doaj.art-92a5ea55fec14d959efb0cfaaae4be33 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-20T08:18:59Z |
| publishDate | 2021-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-92a5ea55fec14d959efb0cfaaae4be332022-12-21T19:47:03ZengAIMS PressAIMS Mathematics2473-69882021-01-01632579258910.3934/math.2021156A simple method for solving matrix equations $ AXB = D $ and $ GXH = C $Huiting Zhang0Hairui Zhang1Lina Liu2Yongxin Yuan3School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, ChinaSchool of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, ChinaSchool of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, ChinaSchool of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, ChinaA simple method to solve the common solution to the pair of linear matrix equations $ AXB = D $ and $ GXH = C $ is introduced. Some necessary and sufficient conditions for the existence of a common solution, and two expressions for the general common solution of the equation pair are provided by the proposed method. Subsequently, the results are applied to determine the solution of the matrix equation $ AXB+GYH = D $ and the Hermitian solution of the matrix equation $ AXB = D. $http://awstest.aimspress.com/article/doi/10.3934/math.2021156?viewType=HTMLmatrix equationgeneralized inversecommon solutionhermitian solution |
| spellingShingle | Huiting Zhang Hairui Zhang Lina Liu Yongxin Yuan A simple method for solving matrix equations $ AXB = D $ and $ GXH = C $ AIMS Mathematics matrix equation generalized inverse common solution hermitian solution |
| title | A simple method for solving matrix equations $ AXB = D $ and $ GXH = C $ |
| title_full | A simple method for solving matrix equations $ AXB = D $ and $ GXH = C $ |
| title_fullStr | A simple method for solving matrix equations $ AXB = D $ and $ GXH = C $ |
| title_full_unstemmed | A simple method for solving matrix equations $ AXB = D $ and $ GXH = C $ |
| title_short | A simple method for solving matrix equations $ AXB = D $ and $ GXH = C $ |
| title_sort | simple method for solving matrix equations axb d and gxh c |
| topic | matrix equation generalized inverse common solution hermitian solution |
| url | http://awstest.aimspress.com/article/doi/10.3934/math.2021156?viewType=HTML |
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