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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/2510.13676 |
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| _version_ | 1866912649784066048 |
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| author | Tsilevich, Natalia Manor, Yahel |
| author_facet | Tsilevich, Natalia Manor, Yahel |
| contents | We introduce the notion of $GL(n)$-dependence of matrices, which is a generalization of linear dependence taking into account the matrix structure. Then we prove a theorem, which generalizes, on the one hand, the fact that $n+1$ vectors in an $n$-dimensional vector space are linearly dependent and, on the other hand, the fact that the natural action of the group $GL(n,{\cal K})$ on ${\cal K}^n\setminus\{0\}$ is transitive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_13676 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $GL(n)$-dependence of matrices Tsilevich, Natalia Manor, Yahel Rings and Algebras We introduce the notion of $GL(n)$-dependence of matrices, which is a generalization of linear dependence taking into account the matrix structure. Then we prove a theorem, which generalizes, on the one hand, the fact that $n+1$ vectors in an $n$-dimensional vector space are linearly dependent and, on the other hand, the fact that the natural action of the group $GL(n,{\cal K})$ on ${\cal K}^n\setminus\{0\}$ is transitive. |
| title | $GL(n)$-dependence of matrices |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2510.13676 |