Row completion of polynomial and rational matrices
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910910937825280 |
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| author | Amparan, Agurtzane Baragaña, Itziar Marcaida, Silvia Roca, Alicia |
| author_facet | Amparan, Agurtzane Baragaña, Itziar Marcaida, Silvia Roca, Alicia |
| contents | We characterize the existence of a polynomial (rational) matrix when its eigenstructure (complete structural data) and some of its rows are prescribed. For polynomial matrices, this problem was solved in a previous work when the polynomial matrix has the same degree as the prescribed submatrix. In that paper, the following row completion problems were also solved arising when the eigenstructure was partially prescribed, keeping the restriction on the degree: the eigenstructure but the row (column) minimal indices, and the finite and/or infinite structures. Here we remove the restriction on the degree, allowing it to be greater than or equal to that of the submatrix. We also generalize the results to rational matrices. Obviously, the results obtained hold for the corresponding column completion problems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_10303 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Row completion of polynomial and rational matrices Amparan, Agurtzane Baragaña, Itziar Marcaida, Silvia Roca, Alicia Spectral Theory 15A54, 15A83, 93B18 We characterize the existence of a polynomial (rational) matrix when its eigenstructure (complete structural data) and some of its rows are prescribed. For polynomial matrices, this problem was solved in a previous work when the polynomial matrix has the same degree as the prescribed submatrix. In that paper, the following row completion problems were also solved arising when the eigenstructure was partially prescribed, keeping the restriction on the degree: the eigenstructure but the row (column) minimal indices, and the finite and/or infinite structures. Here we remove the restriction on the degree, allowing it to be greater than or equal to that of the submatrix. We also generalize the results to rational matrices. Obviously, the results obtained hold for the corresponding column completion problems. |
| title | Row completion of polynomial and rational matrices |
| topic | Spectral Theory 15A54, 15A83, 93B18 |
| url | https://arxiv.org/abs/2504.10303 |