A criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations
We establish that a pair A, B, of nonsingular matrices over a commutative domain R of principal ideals can be reduced to their canonical diagonal forms D A and D B by the common transformation of rows and separate transformations of columns. This means that there exist invertible matrices U, V A, an...
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| Datum: | 1997 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1997
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5074 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511269832884224 |
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| author | Petrichkovich, V. M. Петричкович, В. М. |
| author_facet | Petrichkovich, V. M. Петричкович, В. М. |
| author_sort | Petrichkovich, V. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:24:02Z |
| description | We establish that a pair A, B, of nonsingular matrices over a commutative domain R of principal ideals can be reduced to their canonical diagonal forms D A and D B by the common transformation of rows and separate transformations of columns. This means that there exist invertible matrices U, V A, and V B over R such that UAV a=DA and UAV B=DB if and only if the matrices B *A and D * B DA where B * 0 is the matrix adjoint to B, are equivalent. |
| first_indexed | 2026-03-24T03:10:13Z |
| format | Article |
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| id | umjimathkievua-article-5074 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:10:13Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/ec/838b061bded41ba3ef6fe281a94947ec.pdf |
| spelling | umjimathkievua-article-50742020-03-18T21:24:02Z A criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations Критерій діагоналізовності пари матриць над кільцем головних ідеалів спільними рядковими і різними стовпцевими перетвореннями Petrichkovich, V. M. Петричкович, В. М. We establish that a pair A, B, of nonsingular matrices over a commutative domain R of principal ideals can be reduced to their canonical diagonal forms D A and D B by the common transformation of rows and separate transformations of columns. This means that there exist invertible matrices U, V A, and V B over R such that UAV a=DA and UAV B=DB if and only if the matrices B *A and D * B DA where B * 0 is the matrix adjoint to B, are equivalent. Встановлено, що пара A, B неособливих матриць над комутативного областю головних ідеалів R спільними рядковими і різними стовпцевими перетвореннями зводиться до їхніх канонічних діагональних форм D A і D B, тобто існують оборотні матриці $U, V_A, V_B$ над $R$ такі, що $UAV_a=D^A$ and $UAV_B=D^B$ тоді і тільки тоді, коли матриці $B *A$ і $D * B D^A$ еквівалентні, де $B * 0$ — взаємна матриця для матриці $B$. Institute of Mathematics, NAS of Ukraine 1997-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5074 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 6 (1997); 860–862 Український математичний журнал; Том 49 № 6 (1997); 860–862 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5074/6845 https://umj.imath.kiev.ua/index.php/umj/article/view/5074/6846 Copyright (c) 1997 Petrichkovich V. M. |
| spellingShingle | Petrichkovich, V. M. Петричкович, В. М. A criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations |
| title | A criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations |
| title_alt | Критерій діагоналізовності пари матриць над кільцем головних ідеалів спільними рядковими і різними стовпцевими перетвореннями |
| title_full | A criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations |
| title_fullStr | A criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations |
| title_full_unstemmed | A criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations |
| title_short | A criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations |
| title_sort | criterion of diagonalizability of a pair of matrices over the ring of principal ideals by common row and separate column transformations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5074 |
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