Weierstrass structure and eigenvalue placement of regular matrix pencils under low rank perturbations
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866911818719428608 |
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| author | Baragaña, Itziar Roca, Alicia |
| author_facet | Baragaña, Itziar Roca, Alicia |
| contents | We solve the problem of determining the Weierstrass structure of a regular matrix pencil obtained by a low rank perturbation of another regular matrix pencil. We apply the result to find necessary and sufficient conditions for the existence of a low rank perturbation such that the perturbed pencil has prescribed eigenvalues and algebraic multiplicities. The results hold over fields with sufficient number of elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_19666 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weierstrass structure and eigenvalue placement of regular matrix pencils under low rank perturbations Baragaña, Itziar Roca, Alicia Rings and Algebras 15A22, 47A55, 15A18 We solve the problem of determining the Weierstrass structure of a regular matrix pencil obtained by a low rank perturbation of another regular matrix pencil. We apply the result to find necessary and sufficient conditions for the existence of a low rank perturbation such that the perturbed pencil has prescribed eigenvalues and algebraic multiplicities. The results hold over fields with sufficient number of elements. |
| title | Weierstrass structure and eigenvalue placement of regular matrix pencils under low rank perturbations |
| topic | Rings and Algebras 15A22, 47A55, 15A18 |
| url | https://arxiv.org/abs/2403.19666 |