Generalized equivalence of collections of matrices and common divisors of matrices
The collections \((A_{1}, ..., A_{k})\) and \((B_{1}, ..., B_{k})\) of matrices over an adequate ring are called generalized equivalent if \(A_i=UB_iV_i\) for some invertible matrices \(U\) and \(V_{i}, \; i=1, ..., k.\) Some conditions are established under which the finite collection consisting...
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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/992 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543079153008640 |
|---|---|
| author | Petrychkovych, Vasyl M. |
| author_facet | Petrychkovych, Vasyl M. |
| author_sort | Petrychkovych, Vasyl M. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-05-15T05:12:44Z |
| description | The collections \((A_{1}, ..., A_{k})\) and \((B_{1}, ..., B_{k})\) of matrices over an adequate ring are called generalized equivalent if \(A_i=UB_iV_i\) for some invertible matrices \(U\) and \(V_{i}, \; i=1, ..., k.\) Some conditions are established under which the finite collection consisting of the matrix and its the divisors is generalized equivalent to the collection of the matrices of the triangular and diagonal forms. By using these forms the common divisors of matrices is described. |
| first_indexed | 2025-12-02T15:50:35Z |
| format | Article |
| id | admjournalluguniveduua-article-992 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:50:35Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-9922018-05-15T05:12:44Z Generalized equivalence of collections of matrices and common divisors of matrices Petrychkovych, Vasyl M. collection of matrices, generalized equivalence, canonical diagonal form, common divisors 15A33, 15A21, 15A23 The collections \((A_{1}, ..., A_{k})\) and \((B_{1}, ..., B_{k})\) of matrices over an adequate ring are called generalized equivalent if \(A_i=UB_iV_i\) for some invertible matrices \(U\) and \(V_{i}, \; i=1, ..., k.\) Some conditions are established under which the finite collection consisting of the matrix and its the divisors is generalized equivalent to the collection of the matrices of the triangular and diagonal forms. By using these forms the common divisors of matrices is described. Lugansk National Taras Shevchenko University 2018-05-15 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/992 Algebra and Discrete Mathematics; Vol 3, No 2 (2004) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/992/521 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | collection of matrices generalized equivalence canonical diagonal form common divisors 15A33 15A21 15A23 Petrychkovych, Vasyl M. Generalized equivalence of collections of matrices and common divisors of matrices |
| title | Generalized equivalence of collections of matrices and common divisors of matrices |
| title_full | Generalized equivalence of collections of matrices and common divisors of matrices |
| title_fullStr | Generalized equivalence of collections of matrices and common divisors of matrices |
| title_full_unstemmed | Generalized equivalence of collections of matrices and common divisors of matrices |
| title_short | Generalized equivalence of collections of matrices and common divisors of matrices |
| title_sort | generalized equivalence of collections of matrices and common divisors of matrices |
| topic | collection of matrices generalized equivalence canonical diagonal form common divisors 15A33 15A21 15A23 |
| topic_facet | collection of matrices generalized equivalence canonical diagonal form common divisors 15A33 15A21 15A23 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/992 |
| work_keys_str_mv | AT petrychkovychvasylm generalizedequivalenceofcollectionsofmatricesandcommondivisorsofmatrices |