ON THE COMMUTATION MATRIX
The commutation matrix is a matrix that transforms any vec matrix , to vec transpose . In this article, three definitions of the commutation matrix are presented in different ways. It is shown that these three definitions are equivalent. Proof of the equivalent uses the properties in the Kronecke...
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| Format: | Article |
| Language: | English |
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Universitas Pattimura
2023-12-01
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| Series: | Barekeng |
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| Online Access: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/9190 |
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| _version_ | 1849405605789302784 |
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| author | Yanita Yanita Lyra Yulianti |
| author_facet | Yanita Yanita Lyra Yulianti |
| author_sort | Yanita Yanita |
| collection | DOAJ |
| description | The commutation matrix is a matrix that transforms any vec matrix , to vec transpose . In this article, three definitions of the commutation matrix are presented in different ways. It is shown that these three definitions are equivalent. Proof of the equivalent uses the properties in the Kronecker product on the matrix. We also gave the example of the commutation matrix using three ways as Moreover, in this study, we investigate the properties of the commutation matrix related to its transpose and the relation between the vec matrix and the vec transpose matrix using the commutation matrix. We have that the transpose and the inverse of the commutation matrix is its transpose. |
| format | Article |
| id | doaj-art-8d20df3b909f431ab8470a4c90fd8333 |
| institution | Kabale University |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Universitas Pattimura |
| record_format | Article |
| series | Barekeng |
| spelling | doaj-art-8d20df3b909f431ab8470a4c90fd83332025-08-20T03:36:37ZengUniversitas PattimuraBarekeng1978-72272615-30172023-12-011741997201010.30598/barekengvol17iss4pp1997-20109190ON THE COMMUTATION MATRIXYanita Yanita0Lyra Yulianti1Department of Mathematics and Data Science, Faculty of Mathematics and Natural Science, Andalas UniversityDepartment of Mathematics and Data Science, Faculty of Mathematics and Natural Science, Andalas UniversityThe commutation matrix is a matrix that transforms any vec matrix , to vec transpose . In this article, three definitions of the commutation matrix are presented in different ways. It is shown that these three definitions are equivalent. Proof of the equivalent uses the properties in the Kronecker product on the matrix. We also gave the example of the commutation matrix using three ways as Moreover, in this study, we investigate the properties of the commutation matrix related to its transpose and the relation between the vec matrix and the vec transpose matrix using the commutation matrix. We have that the transpose and the inverse of the commutation matrix is its transpose.https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/9190commutation matrixvec matrixvec transpose matrix |
| spellingShingle | Yanita Yanita Lyra Yulianti ON THE COMMUTATION MATRIX Barekeng commutation matrix vec matrix vec transpose matrix |
| title | ON THE COMMUTATION MATRIX |
| title_full | ON THE COMMUTATION MATRIX |
| title_fullStr | ON THE COMMUTATION MATRIX |
| title_full_unstemmed | ON THE COMMUTATION MATRIX |
| title_short | ON THE COMMUTATION MATRIX |
| title_sort | on the commutation matrix |
| topic | commutation matrix vec matrix vec transpose matrix |
| url | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/9190 |
| work_keys_str_mv | AT yanitayanita onthecommutationmatrix AT lyrayulianti onthecommutationmatrix |