Subspaces of matrices with special rank properties

Abstract : Let K be a field and let V be a vector space of finite dimension n over K. We investigate properties of a subspace M of EndK (V ) of dimension n(n − r + 1) in which each non-zero element of M has rank at least r and show that such subspaces exist if K has a cyclic Galois extension of degree n. We also investigate the maximum dimension of a constant rank r subspace of EndK (V ) when K is finite.
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https://hal.archives-ouvertes.fr/hal-00699674
Contributor : Jean-Guillaume Dumas <>
Submitted on : Monday, May 21, 2012 - 2:30:09 PM
Last modification on : Monday, April 8, 2019 - 1:28:02 PM

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Jean-Guillaume Dumas, Roderick Gow, Gary Mcguire, John Sheekey. Subspaces of matrices with special rank properties. Linear Algebra and its Applications, Elsevier, 2010, 433 (1), pp.191-202. ⟨10.1016/j.laa.2010.02.015⟩. ⟨hal-00699674⟩

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