A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application
We derive the solvability conditions and a formula of a general solution to a Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate the necessary and sufficient conditions for the solvability of the quaternion matrix equation, which involves <inline-formula&g...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/10/1758 |
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| author | Long-Sheng Liu Qing-Wen Wang Mahmoud Saad Mehany |
| author_facet | Long-Sheng Liu Qing-Wen Wang Mahmoud Saad Mehany |
| author_sort | Long-Sheng Liu |
| collection | DOAJ |
| description | We derive the solvability conditions and a formula of a general solution to a Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate the necessary and sufficient conditions for the solvability of the quaternion matrix equation, which involves <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Hermicity. We also provide an algorithm with a numerical example to illustrate the main results of this paper. |
| first_indexed | 2024-03-10T03:29:04Z |
| format | Article |
| id | doaj.art-8b4a9af2d2ac4d8da55ef1df654e72eb |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:29:04Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-8b4a9af2d2ac4d8da55ef1df654e72eb2023-11-23T12:02:00ZengMDPI AGMathematics2227-73902022-05-011010175810.3390/math10101758A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an ApplicationLong-Sheng Liu0Qing-Wen Wang1Mahmoud Saad Mehany 2Department of Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaDepartment of Mathematics, Shanghai University, Shanghai 200444, ChinaWe derive the solvability conditions and a formula of a general solution to a Sylvester-type matrix equation over Hamilton quaternions. As an application, we investigate the necessary and sufficient conditions for the solvability of the quaternion matrix equation, which involves <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>η</mi></semantics></math></inline-formula>-Hermicity. We also provide an algorithm with a numerical example to illustrate the main results of this paper.https://www.mdpi.com/2227-7390/10/10/1758matrix equationHamilton quaternion<i>η</i>-Hermitian matrixMoore–Penrose inverserank |
| spellingShingle | Long-Sheng Liu Qing-Wen Wang Mahmoud Saad Mehany A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application Mathematics matrix equation Hamilton quaternion <i>η</i>-Hermitian matrix Moore–Penrose inverse rank |
| title | A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application |
| title_full | A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application |
| title_fullStr | A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application |
| title_full_unstemmed | A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application |
| title_short | A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application |
| title_sort | sylvester type matrix equation over the hamilton quaternions with an application |
| topic | matrix equation Hamilton quaternion <i>η</i>-Hermitian matrix Moore–Penrose inverse rank |
| url | https://www.mdpi.com/2227-7390/10/10/1758 |
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