Solutions of the matrix linear bilateral polynomial equation and their structure
We investigate the row and column structure of solutions of the matrix polynomial equation A(λ)X(λ) + Y (λ)B(λ) = C(λ), where A(λ),B(λ) and C(λ) are the matrices over the ring of polynomials F[λ] with coefficients in field F. We establish the bounds for degrees of the rows and columns which depend o...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/188435 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Solutions of the matrix linear bilateral polynomial equation and their structure / N.S. Dzhaliuk, V.M. Petrychkovych // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 2. — С. 243–251. — Бібліогр.: 14 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862543943246282752 |
|---|---|
| author | Dzhaliuk, N.S. Petrychkovych, V.M. |
| author_facet | Dzhaliuk, N.S. Petrychkovych, V.M. |
| citation_txt | Solutions of the matrix linear bilateral polynomial equation and their structure / N.S. Dzhaliuk, V.M. Petrychkovych // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 2. — С. 243–251. — Бібліогр.: 14 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| description | We investigate the row and column structure of solutions of the matrix polynomial equation A(λ)X(λ) + Y (λ)B(λ) = C(λ), where A(λ),B(λ) and C(λ) are the matrices over the ring of polynomials F[λ] with coefficients in field F. We establish the bounds for degrees of the rows and columns which depend on degrees of the corresponding invariant factors of matrices A(λ) and B(λ). A criterion for uniqueness of such solutions is pointed out. A method for construction of such solutions is suggested. We also established the existence of solutions of this matrix polynomial equation whose degrees are less than degrees of the Smith normal forms of matrices A(λ) and B(λ).
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| first_indexed | 2025-11-25T00:18:43Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-188435 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-25T00:18:43Z |
| publishDate | 2019 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Dzhaliuk, N.S. Petrychkovych, V.M. 2023-03-01T15:40:21Z 2023-03-01T15:40:21Z 2019 Solutions of the matrix linear bilateral polynomial equation and their structure / N.S. Dzhaliuk, V.M. Petrychkovych // Algebra and Discrete Mathematics. — 2019. — Vol. 27, № 2. — С. 243–251. — Бібліогр.: 14 назв. — англ. 1726-3255 2010 MSC: 15A21, 15A24. https://nasplib.isofts.kiev.ua/handle/123456789/188435 We investigate the row and column structure of solutions of the matrix polynomial equation A(λ)X(λ) + Y (λ)B(λ) = C(λ), where A(λ),B(λ) and C(λ) are the matrices over the ring of polynomials F[λ] with coefficients in field F. We establish the bounds for degrees of the rows and columns which depend on degrees of the corresponding invariant factors of matrices A(λ) and B(λ). A criterion for uniqueness of such solutions is pointed out. A method for construction of such solutions is suggested. We also established the existence of solutions of this matrix polynomial equation whose degrees are less than degrees of the Smith normal forms of matrices A(λ) and B(λ). This work was supported by the budget program of Ukraine “Support for the development of priority research areas” (CPCEC 6541230). en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Solutions of the matrix linear bilateral polynomial equation and their structure Article published earlier |
| spellingShingle | Solutions of the matrix linear bilateral polynomial equation and their structure Dzhaliuk, N.S. Petrychkovych, V.M. |
| title | Solutions of the matrix linear bilateral polynomial equation and their structure |
| title_full | Solutions of the matrix linear bilateral polynomial equation and their structure |
| title_fullStr | Solutions of the matrix linear bilateral polynomial equation and their structure |
| title_full_unstemmed | Solutions of the matrix linear bilateral polynomial equation and their structure |
| title_short | Solutions of the matrix linear bilateral polynomial equation and their structure |
| title_sort | solutions of the matrix linear bilateral polynomial equation and their structure |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188435 |
| work_keys_str_mv | AT dzhaliukns solutionsofthematrixlinearbilateralpolynomialequationandtheirstructure AT petrychkovychvm solutionsofthematrixlinearbilateralpolynomialequationandtheirstructure |