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

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 $-1$.

3 pages, no figures