Row or column completion of polynomial matrices of given degree
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916116699283456 |
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| author | Amparan, A. Baragaña, I. Marcaida, S. Roca, A. |
| author_facet | Amparan, A. Baragaña, I. Marcaida, S. Roca, A. |
| contents | We solve the problem of characterizing the existence of a polynomial matrix of fixed degree when its eigenstructure (or part of it) and some of its rows (columns) are prescribed. More specifically, we present a solution to the row (column) completion problem of a polynomial matrix of given degree under different prescribed invariants: the whole eigenstructure, all of it but the row (column) minimal indices, and the finite and/or infinite structures. Moreover, we characterize the existence of a polynomial matrix with prescribed degree and eigenstructure over an arbitrary field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_06104 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Row or column completion of polynomial matrices of given degree Amparan, A. Baragaña, I. Marcaida, S. Roca, A. Rings and Algebras 15A18, 15A54, 15A83, 93B18 We solve the problem of characterizing the existence of a polynomial matrix of fixed degree when its eigenstructure (or part of it) and some of its rows (columns) are prescribed. More specifically, we present a solution to the row (column) completion problem of a polynomial matrix of given degree under different prescribed invariants: the whole eigenstructure, all of it but the row (column) minimal indices, and the finite and/or infinite structures. Moreover, we characterize the existence of a polynomial matrix with prescribed degree and eigenstructure over an arbitrary field. |
| title | Row or column completion of polynomial matrices of given degree |
| topic | Rings and Algebras 15A18, 15A54, 15A83, 93B18 |
| url | https://arxiv.org/abs/2306.06104 |