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- W1736202723 abstract "Let $mathbb{D}$ be a division ring and $mathbb{F}$ be a subfield of the center of $mathbb{D}$ over which $mathbb{D}$ has finite dimension $d$. Let $n,p,r$ be positive integers and $mathcal{V}$ be an affine subspace of the $mathbb{F}$-vector space $M_{n,p}(mathbb{D})$ in which every matrix has rank less than or equal to $r$. Using a new method, we prove that $dim_{mathbb{F}} mathcal{V} leq max(n,p),rd$ and we characterize the spaces for which equality holds. This extends a famous theorem of Flanders which was known only for fields." @default.
- W1736202723 created "2016-06-24" @default.
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- W1736202723 date "2015-04-08" @default.
- W1736202723 modified "2023-09-26" @default.
- W1736202723 title "The Flanders theorem over division rings" @default.
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