GL(n)-dependence of matrices

2025/10/15 by Tsilevich, Natalia, Manor, Yahel
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2510.13676

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 Kⁿ∖\0\ is transitive.

Citations

• Lifting with Inner Functions of Polynomial Discrepancy
• Regularly weakly based modules over right perfect rings and Dedekind domains

Related

• Large dimensional classical groups and linear spaces
• Relations between O(n)-invariants of several matrices
• Transitivity in finite general linear groups
• On n-dependent groups and fields III. Multilinear forms and invariant connected components
• Computing with matrix invariants