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arXiv · 2510.13676

$GL(n)$-dependence of matrices

Natalia Tsilevich·Yahel Manor
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Abstract

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.

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Natalia Tsilevich, Yahel Manor. 2025-10-15. $GL(n)$-dependence of matrices. https://arxiv.org/abs/2510.13676

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