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- W2019454893 abstract "Let K be a field and let Mm×n(K) denote the space of m×n matrices over K. We investigate properties of a subspace M of Mm×n(K) of dimension n(m-r+1) in which each non-zero element of M has rank at least r and enumerate the number of elements of a given rank in M when K is finite. We also provide an upper bound for the dimension of a constant rank r subspace of Mm×n(K) when K is finite and give non-trivial examples to show that our bound is optimal in some cases. We include a similar a bound for the maximum dimension of a constant rank subspace of skew-symmetric matrices over a finite field." @default.
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- W2019454893 date "2010-07-01" @default.
- W2019454893 modified "2023-10-14" @default.
- W2019454893 title "Subspaces of matrices with special rank properties" @default.
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- W2019454893 doi "https://doi.org/10.1016/j.laa.2010.02.015" @default.
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