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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.10926 |
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| _version_ | 1866912233511976960 |
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| author | Bongartz, Klaus |
| author_facet | Bongartz, Klaus |
| contents | We answer two questions posed 1998 in the book 'Arnolds problems'. First, over any field k there is a representative system for the similarity classes of nxn-matrices which is a finite disjoint union of affine subspaces. And second, for n>1 an analogous statement fails for pairs of nxn-matrices over any algebraically closed field of characteristic 0. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10926 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On normal forms for the similarity classes of matrices and pairs of matrices Bongartz, Klaus Representation Theory We answer two questions posed 1998 in the book 'Arnolds problems'. First, over any field k there is a representative system for the similarity classes of nxn-matrices which is a finite disjoint union of affine subspaces. And second, for n>1 an analogous statement fails for pairs of nxn-matrices over any algebraically closed field of characteristic 0. |
| title | On normal forms for the similarity classes of matrices and pairs of matrices |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2502.10926 |