Four symmetric systems of the matrix equations with an application over the Hamilton quaternions
In this paper, we established some necessary and sufficient conditions for the four symmetric systems to be consistent. Moreover, we derived the expressions of their general solutions when they were solvable. As an application, we investigated the solvability conditions of matrix equations involving...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241607 |
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| author | Long-Sheng Liu Shuo Zhang Hai-Xia Chang |
| author_facet | Long-Sheng Liu Shuo Zhang Hai-Xia Chang |
| author_sort | Long-Sheng Liu |
| collection | DOAJ |
| description | In this paper, we established some necessary and sufficient conditions for the four symmetric systems to be consistent. Moreover, we derived the expressions of their general solutions when they were solvable. As an application, we investigated the solvability conditions of matrix equations involving $ \eta $-Hermicity matrices. Finally, we presented an example to illustrate the main results of this paper. |
| format | Article |
| id | doaj-art-0d3eb483e5a149f38abefd70dde240a1 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-0d3eb483e5a149f38abefd70dde240a12025-01-23T07:53:24ZengAIMS PressAIMS Mathematics2473-69882024-11-01912336623369110.3934/math.20241607Four symmetric systems of the matrix equations with an application over the Hamilton quaternionsLong-Sheng Liu0Shuo Zhang1Hai-Xia Chang2School of Mathematics and Physics, Anqing Normal University, Anqing 246011, ChinaSchool of Mathematics and Physics, Anqing Normal University, Anqing 246011, ChinaSchool of Statistics and Mathematics, Shanghai Lixin University of Accounting and Finance, Shanghai 201209, ChinaIn this paper, we established some necessary and sufficient conditions for the four symmetric systems to be consistent. Moreover, we derived the expressions of their general solutions when they were solvable. As an application, we investigated the solvability conditions of matrix equations involving $ \eta $-Hermicity matrices. Finally, we presented an example to illustrate the main results of this paper.https://www.aimspress.com/article/doi/10.3934/math.20241607matrix equationquaternionmoore-penroserank$ \eta $-hermitian matrix |
| spellingShingle | Long-Sheng Liu Shuo Zhang Hai-Xia Chang Four symmetric systems of the matrix equations with an application over the Hamilton quaternions AIMS Mathematics matrix equation quaternion moore-penrose rank $ \eta $-hermitian matrix |
| title | Four symmetric systems of the matrix equations with an application over the Hamilton quaternions |
| title_full | Four symmetric systems of the matrix equations with an application over the Hamilton quaternions |
| title_fullStr | Four symmetric systems of the matrix equations with an application over the Hamilton quaternions |
| title_full_unstemmed | Four symmetric systems of the matrix equations with an application over the Hamilton quaternions |
| title_short | Four symmetric systems of the matrix equations with an application over the Hamilton quaternions |
| title_sort | four symmetric systems of the matrix equations with an application over the hamilton quaternions |
| topic | matrix equation quaternion moore-penrose rank $ \eta $-hermitian matrix |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241607 |
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