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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/2505.02083 |
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| _version_ | 1866918008622940160 |
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| author | De Terán, Fernando Dopico, Froilán M. Pagacz, Patryk |
| author_facet | De Terán, Fernando Dopico, Froilán M. Pagacz, Patryk |
| contents | We prove that, given two matrix pencils $L$ and $M$, if $M$ belongs to the closure of the orbit of $L$ under strict equivalence, then the dimension of the orbit of $M$ is smaller than or equal to the dimension of the orbit of $L$, and the equality is only attained when $M$ belongs to the orbit of $L$. Our proof uses only the majorization involving the eigenstructures of $L$ and $M$ which characterizes the inclusion relationship between orbit closures, together with the formula for the codimension of the orbit of a pencil in terms of its eigenstruture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02083 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the dimension of orbits of matrix pencils under strict equivalence De Terán, Fernando Dopico, Froilán M. Pagacz, Patryk Spectral Theory 15A18, 15A21, 15A22, 15A54, 65F15 We prove that, given two matrix pencils $L$ and $M$, if $M$ belongs to the closure of the orbit of $L$ under strict equivalence, then the dimension of the orbit of $M$ is smaller than or equal to the dimension of the orbit of $L$, and the equality is only attained when $M$ belongs to the orbit of $L$. Our proof uses only the majorization involving the eigenstructures of $L$ and $M$ which characterizes the inclusion relationship between orbit closures, together with the formula for the codimension of the orbit of a pencil in terms of its eigenstruture. |
| title | On the dimension of orbits of matrix pencils under strict equivalence |
| topic | Spectral Theory 15A18, 15A21, 15A22, 15A54, 65F15 |
| url | https://arxiv.org/abs/2505.02083 |