Solving reduced biquaternion matrices equation $ \sum\limits_{i = 1}^{k}A_iXB_i = C $ with special structure based on semi-tensor product of matrices
In this paper, we propose a real vector representation of reduced quaternion matrix and study its properties. By using this real vector representation, Moore-Penrose inverse, and semi-tensor product of matrices, we study some kinds of solutions of reduced biquaternion matrix equation (1.1). Several...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022181?viewType=HTML |
| _version_ | 1819282335188647936 |
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| author | Wenxv Ding Ying Li Anli Wei Zhihong Liu |
| author_facet | Wenxv Ding Ying Li Anli Wei Zhihong Liu |
| author_sort | Wenxv Ding |
| collection | DOAJ |
| description | In this paper, we propose a real vector representation of reduced quaternion matrix and study its properties. By using this real vector representation, Moore-Penrose inverse, and semi-tensor product of matrices, we study some kinds of solutions of reduced biquaternion matrix equation (1.1). Several numerical examples show that the proposed algorithm is feasible at last. |
| first_indexed | 2024-12-24T01:13:57Z |
| format | Article |
| id | doaj.art-8cf5905ff601495ca5920473b7b7c458 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-24T01:13:57Z |
| publishDate | 2022-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-8cf5905ff601495ca5920473b7b7c4582022-12-21T17:22:48ZengAIMS PressAIMS Mathematics2473-69882022-01-01733258327610.3934/math.2022181Solving reduced biquaternion matrices equation $ \sum\limits_{i = 1}^{k}A_iXB_i = C $ with special structure based on semi-tensor product of matricesWenxv Ding0Ying Li1Anli Wei2Zhihong Liu31. College of Mathematical Sciences, Liaocheng University, Liaocheng 252000, China 2. Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng 252000, China1. College of Mathematical Sciences, Liaocheng University, Liaocheng 252000, China 2. Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng 252000, China1. College of Mathematical Sciences, Liaocheng University, Liaocheng 252000, China 2. Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng 252000, China1. College of Mathematical Sciences, Liaocheng University, Liaocheng 252000, China 2. Research Center of Semi-tensor Product of Matrices: Theory and Applications, Liaocheng 252000, ChinaIn this paper, we propose a real vector representation of reduced quaternion matrix and study its properties. By using this real vector representation, Moore-Penrose inverse, and semi-tensor product of matrices, we study some kinds of solutions of reduced biquaternion matrix equation (1.1). Several numerical examples show that the proposed algorithm is feasible at last.https://www.aimspress.com/article/doi/10.3934/math.2022181?viewType=HTMLsemi-tensor product of matricesreduced biquaternionmatrix equationreal vector representation |
| spellingShingle | Wenxv Ding Ying Li Anli Wei Zhihong Liu Solving reduced biquaternion matrices equation $ \sum\limits_{i = 1}^{k}A_iXB_i = C $ with special structure based on semi-tensor product of matrices AIMS Mathematics semi-tensor product of matrices reduced biquaternion matrix equation real vector representation |
| title | Solving reduced biquaternion matrices equation $ \sum\limits_{i = 1}^{k}A_iXB_i = C $ with special structure based on semi-tensor product of matrices |
| title_full | Solving reduced biquaternion matrices equation $ \sum\limits_{i = 1}^{k}A_iXB_i = C $ with special structure based on semi-tensor product of matrices |
| title_fullStr | Solving reduced biquaternion matrices equation $ \sum\limits_{i = 1}^{k}A_iXB_i = C $ with special structure based on semi-tensor product of matrices |
| title_full_unstemmed | Solving reduced biquaternion matrices equation $ \sum\limits_{i = 1}^{k}A_iXB_i = C $ with special structure based on semi-tensor product of matrices |
| title_short | Solving reduced biquaternion matrices equation $ \sum\limits_{i = 1}^{k}A_iXB_i = C $ with special structure based on semi-tensor product of matrices |
| title_sort | solving reduced biquaternion matrices equation sum limits i 1 k a ixb i c with special structure based on semi tensor product of matrices |
| topic | semi-tensor product of matrices reduced biquaternion matrix equation real vector representation |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022181?viewType=HTML |
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