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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.12433 |
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| _version_ | 1866916653713850368 |
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| author | De Terán, Fernando Iannazzo, Bruno |
| author_facet | De Terán, Fernando Iannazzo, Bruno |
| contents | We provide a characterization for a periodic system of generalized Sylvester and conjugate-Sylvester equations, with at most one generalized conjugate-Sylvester equation, to have a unique solution when all coefficient matrices are square and all unknown matrices of the system have the same size. We also present a procedure to reduce an arbitrary system of generalized Sylvester and conjugate-Sylvester equations to periodic systems having at most one generalized conjugate-Sylvester equation. Therefore, the obtained characterization for the uniqueness of solution of periodic systems provides a characterization for general systems of generalized Sylvester and conjugate-Sylvester equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12433 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniqueness of solution of systems of generalized Sylvester and conjugate-Sylvester equations De Terán, Fernando Iannazzo, Bruno Rings and Algebras 15A22, 15A24, 65F15 We provide a characterization for a periodic system of generalized Sylvester and conjugate-Sylvester equations, with at most one generalized conjugate-Sylvester equation, to have a unique solution when all coefficient matrices are square and all unknown matrices of the system have the same size. We also present a procedure to reduce an arbitrary system of generalized Sylvester and conjugate-Sylvester equations to periodic systems having at most one generalized conjugate-Sylvester equation. Therefore, the obtained characterization for the uniqueness of solution of periodic systems provides a characterization for general systems of generalized Sylvester and conjugate-Sylvester equations. |
| title | Uniqueness of solution of systems of generalized Sylvester and conjugate-Sylvester equations |
| topic | Rings and Algebras 15A22, 15A24, 65F15 |
| url | https://arxiv.org/abs/2503.12433 |