Subspaces of Matrices with Special Rank Properties
نویسندگان
چکیده
Let K be a field and let V be a vector space of finite dimension n over K. We investigate properties of a subspaceM 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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