On the Low-Degree Solution of the Sylvester Matrix Polynomial Equation
We study the low-degree solution of the Sylvester matrix equation A1λ+A0Xλ+YλB1λ+B0=C0, where A1λ+A0 and B1λ+B0 are regular. Using the substitution of parameter variables λ, we assume that the matrices A0 and B0 are invertible. Thus, we prove that if the equation is solvable, then it has a low-degre...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/4612177 |
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| _version_ | 1832556885309390848 |
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| author | Yunbo Tian Chao Xia |
| author_facet | Yunbo Tian Chao Xia |
| author_sort | Yunbo Tian |
| collection | DOAJ |
| description | We study the low-degree solution of the Sylvester matrix equation A1λ+A0Xλ+YλB1λ+B0=C0, where A1λ+A0 and B1λ+B0 are regular. Using the substitution of parameter variables λ, we assume that the matrices A0 and B0 are invertible. Thus, we prove that if the equation is solvable, then it has a low-degree solution Lλ,Mλ, satisfying the degree conditions δLλ<IndA0−1A1 and δMλ<IndB1B0−1. |
| format | Article |
| id | doaj-art-4cf0f5785e8b4f86ba3a2e1f9cf37b7d |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-4cf0f5785e8b4f86ba3a2e1f9cf37b7d2025-02-03T05:44:09ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/46121774612177On the Low-Degree Solution of the Sylvester Matrix Polynomial EquationYunbo Tian0Chao Xia1School of Mathematics and Statistics, Linyi University, Linyi, Shandong 276000, ChinaSchool of Mathematics and Statistics, Changchun University of Technology, Changchun, ChinaWe study the low-degree solution of the Sylvester matrix equation A1λ+A0Xλ+YλB1λ+B0=C0, where A1λ+A0 and B1λ+B0 are regular. Using the substitution of parameter variables λ, we assume that the matrices A0 and B0 are invertible. Thus, we prove that if the equation is solvable, then it has a low-degree solution Lλ,Mλ, satisfying the degree conditions δLλ<IndA0−1A1 and δMλ<IndB1B0−1.http://dx.doi.org/10.1155/2021/4612177 |
| spellingShingle | Yunbo Tian Chao Xia On the Low-Degree Solution of the Sylvester Matrix Polynomial Equation Journal of Mathematics |
| title | On the Low-Degree Solution of the Sylvester Matrix Polynomial Equation |
| title_full | On the Low-Degree Solution of the Sylvester Matrix Polynomial Equation |
| title_fullStr | On the Low-Degree Solution of the Sylvester Matrix Polynomial Equation |
| title_full_unstemmed | On the Low-Degree Solution of the Sylvester Matrix Polynomial Equation |
| title_short | On the Low-Degree Solution of the Sylvester Matrix Polynomial Equation |
| title_sort | on the low degree solution of the sylvester matrix polynomial equation |
| url | http://dx.doi.org/10.1155/2021/4612177 |
| work_keys_str_mv | AT yunbotian onthelowdegreesolutionofthesylvestermatrixpolynomialequation AT chaoxia onthelowdegreesolutionofthesylvestermatrixpolynomialequation |