On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor Product
MM-2 semitensor product is a new and very useful mathematical tool, which breaks the limitation of traditional matrix multiplication on the dimension of matrices and has a wide application prospect. This article aims to investigate the solutions of the matrix equation A°lX=B with respect to MM-2 sem...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/6651434 |
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| _version_ | 1832546784650461184 |
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| author | Jin Wang |
| author_facet | Jin Wang |
| author_sort | Jin Wang |
| collection | DOAJ |
| description | MM-2 semitensor product is a new and very useful mathematical tool, which breaks the limitation of traditional matrix multiplication on the dimension of matrices and has a wide application prospect. This article aims to investigate the solutions of the matrix equation A°lX=B with respect to MM-2 semitensor product. The case where the solutions of the equation are vectors is discussed first. Compatible conditions of matrices and the necessary and sufficient condition for the solvability is studied successively. Furthermore, concrete methods of solving the equation are provided. Then, the case where the solutions of the equation are matrices is studied in a similar way. Finally, several examples are given to illustrate the efficiency of the results. |
| format | Article |
| id | doaj-art-1269989c484e4814a44bfb97516dbbc9 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-1269989c484e4814a44bfb97516dbbc92025-02-03T06:47:03ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/66514346651434On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor ProductJin Wang0School of Mathematics, Shandong University, Jinan 250199, ChinaMM-2 semitensor product is a new and very useful mathematical tool, which breaks the limitation of traditional matrix multiplication on the dimension of matrices and has a wide application prospect. This article aims to investigate the solutions of the matrix equation A°lX=B with respect to MM-2 semitensor product. The case where the solutions of the equation are vectors is discussed first. Compatible conditions of matrices and the necessary and sufficient condition for the solvability is studied successively. Furthermore, concrete methods of solving the equation are provided. Then, the case where the solutions of the equation are matrices is studied in a similar way. Finally, several examples are given to illustrate the efficiency of the results.http://dx.doi.org/10.1155/2021/6651434 |
| spellingShingle | Jin Wang On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor Product Journal of Mathematics |
| title | On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor Product |
| title_full | On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor Product |
| title_fullStr | On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor Product |
| title_full_unstemmed | On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor Product |
| title_short | On Solutions of the Matrix Equation A∘lX = B with respect to MM-2 Semitensor Product |
| title_sort | on solutions of the matrix equation a∘lx b with respect to mm 2 semitensor product |
| url | http://dx.doi.org/10.1155/2021/6651434 |
| work_keys_str_mv | AT jinwang onsolutionsofthematrixequationalxbwithrespecttomm2semitensorproduct |