Research on Least-Square η-Hermitian Solutions of Split Quaternion Matrix Equations
In this article, we use the real representation matrix of the split quaternion matrix, vector operator, Kronecker product, and Moore–Penrose generalized inverse. We establish the least norm expression of the least-square η-Hermitian solution and the least norm expression of the least-square η-anti-H...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/9713495 |
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| _version_ | 1849305974201909248 |
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| author | Yang Zhang Xiaoda Zhang |
| author_facet | Yang Zhang Xiaoda Zhang |
| author_sort | Yang Zhang |
| collection | DOAJ |
| description | In this article, we use the real representation matrix of the split quaternion matrix, vector operator, Kronecker product, and Moore–Penrose generalized inverse. We establish the least norm expression of the least-square η-Hermitian solution and the least norm expression of the least-square η-anti-Hermitian solution on the split quaternion of the matrix equation AXB+CXD=E. The final solution expression is represented only by real matrices and real vectors. In the algorithm, only real number operations are involved, which avoids complex quaternion operations and greatly reduces the amount of computation. Finally, we use two examples to verify the effectiveness of the proposed algorithm. |
| format | Article |
| id | doaj-art-33aa4077d45f455d9f6bbe8c23e8655c |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-33aa4077d45f455d9f6bbe8c23e8655c2025-08-20T03:55:15ZengWileyJournal of Mathematics2314-47852024-01-01202410.1155/2024/9713495Research on Least-Square η-Hermitian Solutions of Split Quaternion Matrix EquationsYang Zhang0Xiaoda Zhang1Northeast Forestry UniversityNortheast Forestry UniversityIn this article, we use the real representation matrix of the split quaternion matrix, vector operator, Kronecker product, and Moore–Penrose generalized inverse. We establish the least norm expression of the least-square η-Hermitian solution and the least norm expression of the least-square η-anti-Hermitian solution on the split quaternion of the matrix equation AXB+CXD=E. The final solution expression is represented only by real matrices and real vectors. In the algorithm, only real number operations are involved, which avoids complex quaternion operations and greatly reduces the amount of computation. Finally, we use two examples to verify the effectiveness of the proposed algorithm.http://dx.doi.org/10.1155/2024/9713495 |
| spellingShingle | Yang Zhang Xiaoda Zhang Research on Least-Square η-Hermitian Solutions of Split Quaternion Matrix Equations Journal of Mathematics |
| title | Research on Least-Square η-Hermitian Solutions of Split Quaternion Matrix Equations |
| title_full | Research on Least-Square η-Hermitian Solutions of Split Quaternion Matrix Equations |
| title_fullStr | Research on Least-Square η-Hermitian Solutions of Split Quaternion Matrix Equations |
| title_full_unstemmed | Research on Least-Square η-Hermitian Solutions of Split Quaternion Matrix Equations |
| title_short | Research on Least-Square η-Hermitian Solutions of Split Quaternion Matrix Equations |
| title_sort | research on least square η hermitian solutions of split quaternion matrix equations |
| url | http://dx.doi.org/10.1155/2024/9713495 |
| work_keys_str_mv | AT yangzhang researchonleastsquareēhermitiansolutionsofsplitquaternionmatrixequations AT xiaodazhang researchonleastsquareēhermitiansolutionsofsplitquaternionmatrixequations |