Row or column completion of polynomial matrices of given degree II
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916116812529664 |
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| author | Amparan, Agurtzane Baragaña, Itziar Marcaida, Silvia Roca, Alicia |
| author_facet | Amparan, Agurtzane Baragaña, Itziar Marcaida, Silvia Roca, Alicia |
| contents | The row (column) completion problem of polynomial matrices of given degree with prescribed eigenstructure has been studied in \cite{AmBaMaRo23}, where several results of prescription of some of the four types of invariants that form the eigenstructure have also been obtained. In this paper we conclude the study, solving the completion for the cases not covered there. More precisely, the row completion problem of a polynomial matrix is solved when we prescribe the infinite (finite) structure and column and/or row minimal indices, and finally the column and/or row minimal indices. The necessity of the characterizations obtained holds to be true over arbitrary fields in all cases, whilst to prove the sufficiency it is required, in some of the cases, to work over algebraically closed fields. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_08408 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Row or column completion of polynomial matrices of given degree II Amparan, Agurtzane Baragaña, Itziar Marcaida, Silvia Roca, Alicia Rings and Algebras 15A18, 15A54, 15A83 The row (column) completion problem of polynomial matrices of given degree with prescribed eigenstructure has been studied in \cite{AmBaMaRo23}, where several results of prescription of some of the four types of invariants that form the eigenstructure have also been obtained. In this paper we conclude the study, solving the completion for the cases not covered there. More precisely, the row completion problem of a polynomial matrix is solved when we prescribe the infinite (finite) structure and column and/or row minimal indices, and finally the column and/or row minimal indices. The necessity of the characterizations obtained holds to be true over arbitrary fields in all cases, whilst to prove the sufficiency it is required, in some of the cases, to work over algebraically closed fields. |
| title | Row or column completion of polynomial matrices of given degree II |
| topic | Rings and Algebras 15A18, 15A54, 15A83 |
| url | https://arxiv.org/abs/2311.08408 |