Spaces of matrices with few eigenvalues (II)
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913097533358080 |
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| author | Pazzis, Clément de Seguins |
| author_facet | Pazzis, Clément de Seguins |
| contents | Let $F$ be a field, and $\mathcal{M}$ be a linear subspace of $n$-by-$n$ matrices with entries in $F$ that have at most two eigenvalues in $F$ (respectively, at most one non-zero eigenvalue in $F$). In a previous article, we have determined the greatest possible dimension for $\mathcal{M}$ when the characteristic of $F$ is not $2$. In this article and its sequel, we solve this problem for all fields with characteristic $2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05849 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spaces of matrices with few eigenvalues (II) Pazzis, Clément de Seguins Rings and Algebras 15A30, 15A18 Let $F$ be a field, and $\mathcal{M}$ be a linear subspace of $n$-by-$n$ matrices with entries in $F$ that have at most two eigenvalues in $F$ (respectively, at most one non-zero eigenvalue in $F$). In a previous article, we have determined the greatest possible dimension for $\mathcal{M}$ when the characteristic of $F$ is not $2$. In this article and its sequel, we solve this problem for all fields with characteristic $2$. |
| title | Spaces of matrices with few eigenvalues (II) |
| topic | Rings and Algebras 15A30, 15A18 |
| url | https://arxiv.org/abs/2605.05849 |