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Characterizing $(0,\pm 1)$-matrices with only even-rank principal submatrices in terms of skew-symmetry

Published 12 Nov 2018 in math.CO | (1811.04728v2)

Abstract: We show that every principal submatrix of a square matrix $A$ with only entries in ${0,1,-1}$ has even rank if and only if $A$ is skew-symmetric up to multiplication of rows/columns by $-1$.

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