On the uniqueness of the unital divisor of a matrix polynomial over an arbitrary field
Conditions are established under which the unital divisor extracted from a matrix polynomial over an arbitrary field is determined uniquely by its characteristic polynomial. The result obtained is applied to the problem of solving matrix polynomial equations.
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| Date: | 1993 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1993
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5869 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512089381011456 |
|---|---|
| author | Prokip, V. M. Прокіп, В. М. |
| author_facet | Prokip, V. M. Прокіп, В. М. |
| author_sort | Prokip, V. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:19:41Z |
| description | Conditions are established under which the unital divisor extracted from a matrix polynomial over an arbitrary field is determined uniquely by its characteristic polynomial. The result obtained is applied to the problem of solving matrix polynomial equations. |
| first_indexed | 2026-03-24T03:23:14Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5869 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:23:14Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/92/37c825ebd16d6a786c2c9c7516ebdd92.pdf |
| spelling | umjimathkievua-article-58692020-03-19T09:19:41Z On the uniqueness of the unital divisor of a matrix polynomial over an arbitrary field Про єдиність унітального дільника матричного многочлена над довільним полем Prokip, V. M. Прокіп, В. М. Conditions are established under which the unital divisor extracted from a matrix polynomial over an arbitrary field is determined uniquely by its characteristic polynomial. The result obtained is applied to the problem of solving matrix polynomial equations. Встановлено умови, при яких виділений із матричного многочлена над довільним полем унітальний дільник однозначно визначається своїм характеристичним многочленом. Вказано також застосування здобутого результату до розв’язування матричних многочленних рівнянь. Institute of Mathematics, NAS of Ukraine 1993-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5869 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 6 (1993); 803–808 Український математичний журнал; Том 45 № 6 (1993); 803–808 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5869/8421 https://umj.imath.kiev.ua/index.php/umj/article/view/5869/8422 Copyright (c) 1993 Prokip V. M. |
| spellingShingle | Prokip, V. M. Прокіп, В. М. On the uniqueness of the unital divisor of a matrix polynomial over an arbitrary field |
| title | On the uniqueness of the unital divisor of a matrix polynomial over an arbitrary field |
| title_alt | Про єдиність унітального дільника матричного многочлена над довільним полем |
| title_full | On the uniqueness of the unital divisor of a matrix polynomial over an arbitrary field |
| title_fullStr | On the uniqueness of the unital divisor of a matrix polynomial over an arbitrary field |
| title_full_unstemmed | On the uniqueness of the unital divisor of a matrix polynomial over an arbitrary field |
| title_short | On the uniqueness of the unital divisor of a matrix polynomial over an arbitrary field |
| title_sort | on the uniqueness of the unital divisor of a matrix polynomial over an arbitrary field |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5869 |
| work_keys_str_mv | AT prokipvm ontheuniquenessoftheunitaldivisorofamatrixpolynomialoveranarbitraryfield AT prokípvm ontheuniquenessoftheunitaldivisorofamatrixpolynomialoveranarbitraryfield AT prokipvm proêdinístʹunítalʹnogodílʹnikamatričnogomnogočlenanaddovílʹnimpolem AT prokípvm proêdinístʹunítalʹnogodílʹnikamatričnogomnogočlenanaddovílʹnimpolem |