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- W2212584448 abstract "Let $n$ and $p$ be non-negative integers with $n geq p$, and $S$ be a linear subspace of the space of all $n$ by $p$ matrices with entries in a field $mathbb{K}$. A classical theorem of Flanders states that $S$ contains a matrix with rank $p$ whenever $mathrm{codim} S <n$. In this article, we prove the following related result: if $mathrm{codim} S<n-1$, then, for any non-zero $n$ by $p$ matrix $N$ with rank less than $p$, there exists a line that is directed by $N$, has a common point with $S$ and contains only rank $p$ matrices." @default.
- W2212584448 created "2016-06-24" @default.
- W2212584448 creator A5016953630 @default.
- W2212584448 date "2018-01-23" @default.
- W2212584448 modified "2023-09-27" @default.
- W2212584448 title "Lines of full rank matrices in large subspaces" @default.
- W2212584448 cites W2046978501 @default.
- W2212584448 hasPublicationYear "2018" @default.
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