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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| Дата: | 2019 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2019
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
irk-123456789-188435 |
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dspace |
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irk-123456789-1884352023-03-02T01:27:37Z Solutions of the matrix linear bilateral polynomial equation and their structure Dzhaliuk, N.S. Petrychkovych, V.M. 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). 2019 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/188435 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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). |
| format |
Article |
| author |
Dzhaliuk, N.S. Petrychkovych, V.M. |
| spellingShingle |
Dzhaliuk, N.S. Petrychkovych, V.M. Solutions of the matrix linear bilateral polynomial equation and their structure Algebra and Discrete Mathematics |
| author_facet |
Dzhaliuk, N.S. Petrychkovych, V.M. |
| author_sort |
Dzhaliuk, N.S. |
| title |
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_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_sort |
solutions of the matrix linear bilateral polynomial equation and their structure |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2019 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/188435 |
| 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. |
| series |
Algebra and Discrete Mathematics |
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AT dzhaliukns solutionsofthematrixlinearbilateralpolynomialequationandtheirstructure AT petrychkovychvm solutionsofthematrixlinearbilateralpolynomialequationandtheirstructure |
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2023-10-18T23:08:21Z |
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2023-10-18T23:08:21Z |
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1796157348569415680 |