Symmetric Equivalence of Matrix Polynomials and Isolation of a Common Unital Divisor in Matrix Polynomials
We find necessary and sufficient conditions for the existence of common unital divisors with given Smith forms of nonsingular matrix polynomials and common factorization of symmetric matrices over rings of polynomials with involution. We obtain conditions for the symmetric equivalence of such matric...
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| Date: | 2001 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2001
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4236 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510366848516096 |
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| author | Kuchma, M. I. Кучма, М. І. |
| author_facet | Kuchma, M. I. Кучма, М. І. |
| author_sort | Kuchma, M. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:25:08Z |
| description | We find necessary and sufficient conditions for the existence of common unital divisors with given Smith forms of nonsingular matrix polynomials and common factorization of symmetric matrices over rings of polynomials with involution. We obtain conditions for the symmetric equivalence of such matrices. |
| first_indexed | 2026-03-24T02:55:52Z |
| format | Article |
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| id | umjimathkievua-article-4236 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:55:52Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/90/ec75272165a656d6758db30dd112ea90.pdf |
| spelling | umjimathkievua-article-42362020-03-18T20:25:08Z Symmetric Equivalence of Matrix Polynomials and Isolation of a Common Unital Divisor in Matrix Polynomials Симетрична еквівалентність матричних многочленів і виділеиия спільного упітальпого дільника із матричних многочленів Kuchma, M. I. Кучма, М. І. We find necessary and sufficient conditions for the existence of common unital divisors with given Smith forms of nonsingular matrix polynomials and common factorization of symmetric matrices over rings of polynomials with involution. We obtain conditions for the symmetric equivalence of such matrices. Знайдено необхідні та достатні умови існування спільних уиітальпих дільників із заданими формами Сміта пеособливих матричних многочленів, спільної факторизації симетричних матриць над кільцями многочленів з інволюцією. Отримано умови симетричної еквівалентності таких матриць. Institute of Mathematics, NAS of Ukraine 2001-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4236 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 2 (2001); 211-219 Український математичний журнал; Том 53 № 2 (2001); 211-219 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4236/5176 https://umj.imath.kiev.ua/index.php/umj/article/view/4236/5177 Copyright (c) 2001 Kuchma M. I. |
| spellingShingle | Kuchma, M. I. Кучма, М. І. Symmetric Equivalence of Matrix Polynomials and Isolation of a Common Unital Divisor in Matrix Polynomials |
| title | Symmetric Equivalence of Matrix Polynomials and Isolation of a Common Unital Divisor in Matrix Polynomials |
| title_alt | Симетрична еквівалентність матричних многочленів і виділеиия спільного упітальпого дільника із матричних многочленів |
| title_full | Symmetric Equivalence of Matrix Polynomials and Isolation of a Common Unital Divisor in Matrix Polynomials |
| title_fullStr | Symmetric Equivalence of Matrix Polynomials and Isolation of a Common Unital Divisor in Matrix Polynomials |
| title_full_unstemmed | Symmetric Equivalence of Matrix Polynomials and Isolation of a Common Unital Divisor in Matrix Polynomials |
| title_short | Symmetric Equivalence of Matrix Polynomials and Isolation of a Common Unital Divisor in Matrix Polynomials |
| title_sort | symmetric equivalence of matrix polynomials and isolation of a common unital divisor in matrix polynomials |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4236 |
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