On the Kronecker Products and Their Applications
This paper studies the properties of the Kronecker product related to the mixed matrix products, the vector operator, and the vec-permutation matrix and gives several theorems and their proofs. In addition, we establish the relations between the singular values of two matrices and their Kronecker pr...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/296185 |
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| _version_ | 1832548890270760960 |
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| author | Huamin Zhang Feng Ding |
| author_facet | Huamin Zhang Feng Ding |
| author_sort | Huamin Zhang |
| collection | DOAJ |
| description | This paper studies the properties of the Kronecker product related to the mixed matrix products, the vector operator, and the vec-permutation matrix and gives several theorems and their proofs. In addition, we establish the relations between the singular values of two matrices and their Kronecker product and the relations between the determinant, the trace, the rank, and the polynomial matrix of the Kronecker products. |
| format | Article |
| id | doaj-art-6ca73e46cee64f558212d3fdef0476c7 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-6ca73e46cee64f558212d3fdef0476c72025-02-03T06:12:44ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/296185296185On the Kronecker Products and Their ApplicationsHuamin Zhang0Feng Ding1Key Laboratory of Advanced Process Control for Light Industry of Ministry of Education, Jiangnan University, Wuxi 214122, ChinaKey Laboratory of Advanced Process Control for Light Industry of Ministry of Education, Jiangnan University, Wuxi 214122, ChinaThis paper studies the properties of the Kronecker product related to the mixed matrix products, the vector operator, and the vec-permutation matrix and gives several theorems and their proofs. In addition, we establish the relations between the singular values of two matrices and their Kronecker product and the relations between the determinant, the trace, the rank, and the polynomial matrix of the Kronecker products.http://dx.doi.org/10.1155/2013/296185 |
| spellingShingle | Huamin Zhang Feng Ding On the Kronecker Products and Their Applications Journal of Applied Mathematics |
| title | On the Kronecker Products and Their Applications |
| title_full | On the Kronecker Products and Their Applications |
| title_fullStr | On the Kronecker Products and Their Applications |
| title_full_unstemmed | On the Kronecker Products and Their Applications |
| title_short | On the Kronecker Products and Their Applications |
| title_sort | on the kronecker products and their applications |
| url | http://dx.doi.org/10.1155/2013/296185 |
| work_keys_str_mv | AT huaminzhang onthekroneckerproductsandtheirapplications AT fengding onthekroneckerproductsandtheirapplications |