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

2018/11/12 by Robert Brijder, Brijder, Robert
Computer Science · Decision Sciences · Engineering · #Combinatorics (math.CO) #FOS: Mathematics #Fuzzy and Soft Set Theory #Matrix Theory and Algorithms #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1811.04728

openalex publication_date 2018/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Skew-symmetric matrices and their principal minors
• On 0--1 matrices whose inverses have entries of the same modulus
• Even grade generic skew-symmetric matrix polynomials with bounded rank
• Generic skew-symmetric matrix polynomials with fixed rank and fixed odd\n grade
• A transformation that preserves principal minors of skew-symmetric\n matrices