Linear operators that preserve maximal column ranks of nonnegative integer matrices

Song, Seok-zun

doi:10.1090/S0002-9939-98-04308-1

Linear operators that preserve maximal column ranks of nonnegative integer matrices
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Proc. Amer. Math. Soc. 126 (1998), 2205-2211 Request permission

Abstract:

The maximal column rank of an $m$ by $n$ matrix over a semiring is the maximal number of the columns of $A$ which are linearly independent. We characterize the linear operators which preserve the maximal column ranks of nonnegative integer matrices.

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