Symmetrical Multidimensional Matrices and Their Inversion
The article discusses the development of the theory of the multidimensional matrices in the part regarding the symmetrical multidimensional matrices. The symmetry property is considered in terms of the structure of the multidimensional matrix. The so called kq-dimensional symmetrical matrices are co...
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| Format: | Article |
| Language: | Russian |
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Educational institution «Belarusian State University of Informatics and Radioelectronics»
2024-02-01
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| Series: | Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki |
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| Online Access: | https://doklady.bsuir.by/jour/article/view/3854 |
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| _version_ | 1849398491602747392 |
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| author | V. S. Mukha |
| author_facet | V. S. Mukha |
| author_sort | V. S. Mukha |
| collection | DOAJ |
| description | The article discusses the development of the theory of the multidimensional matrices in the part regarding the symmetrical multidimensional matrices. The symmetry property is considered in terms of the structure of the multidimensional matrix. The so called kq-dimensional symmetrical matrices are considered along with the multidimensional symmetrical matrices, i. e. the matrices symmetrical to the multi-indices containing q indices. Unit, unit symmetrical and unit kq-symmetric matrices are considered. The matrices inverse to the multidimensional matrices with respect to the unit, unit symmetrical, and unit kq-symmetrical matrices are defined. It is proven that the matrices, inverse to the multidimensional matrices with respect to the unit symmetrical and unit kq-symmetrical matrices are the Moore–Penrose matrices. The distinct instances are given. |
| format | Article |
| id | doaj-art-8fa71eaea75e412390a4a33c076dc1b1 |
| institution | Kabale University |
| issn | 1729-7648 |
| language | Russian |
| publishDate | 2024-02-01 |
| publisher | Educational institution «Belarusian State University of Informatics and Radioelectronics» |
| record_format | Article |
| series | Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki |
| spelling | doaj-art-8fa71eaea75e412390a4a33c076dc1b12025-08-20T03:38:35ZrusEducational institution «Belarusian State University of Informatics and Radioelectronics»Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki1729-76482024-02-01221222910.35596/1729-7648-2024-22-1-22-291962Symmetrical Multidimensional Matrices and Their InversionV. S. Mukha0Belarusian State University of Informatics and RadioelectronicsThe article discusses the development of the theory of the multidimensional matrices in the part regarding the symmetrical multidimensional matrices. The symmetry property is considered in terms of the structure of the multidimensional matrix. The so called kq-dimensional symmetrical matrices are considered along with the multidimensional symmetrical matrices, i. e. the matrices symmetrical to the multi-indices containing q indices. Unit, unit symmetrical and unit kq-symmetric matrices are considered. The matrices inverse to the multidimensional matrices with respect to the unit, unit symmetrical, and unit kq-symmetrical matrices are defined. It is proven that the matrices, inverse to the multidimensional matrices with respect to the unit symmetrical and unit kq-symmetrical matrices are the Moore–Penrose matrices. The distinct instances are given.https://doklady.bsuir.by/jour/article/view/3854symmetrical multidimensional matrixunit multidimensional matrixinverse multidimensional matrixmultidimensional-matrix polynomialmoore–penrose matrix |
| spellingShingle | V. S. Mukha Symmetrical Multidimensional Matrices and Their Inversion Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioèlektroniki symmetrical multidimensional matrix unit multidimensional matrix inverse multidimensional matrix multidimensional-matrix polynomial moore–penrose matrix |
| title | Symmetrical Multidimensional Matrices and Their Inversion |
| title_full | Symmetrical Multidimensional Matrices and Their Inversion |
| title_fullStr | Symmetrical Multidimensional Matrices and Their Inversion |
| title_full_unstemmed | Symmetrical Multidimensional Matrices and Their Inversion |
| title_short | Symmetrical Multidimensional Matrices and Their Inversion |
| title_sort | symmetrical multidimensional matrices and their inversion |
| topic | symmetrical multidimensional matrix unit multidimensional matrix inverse multidimensional matrix multidimensional-matrix polynomial moore–penrose matrix |
| url | https://doklady.bsuir.by/jour/article/view/3854 |
| work_keys_str_mv | AT vsmukha symmetricalmultidimensionalmatricesandtheirinversion |