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

arXiv: Combinatorics, 2018.

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Abstract:

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

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