Hadamard equivalence via graph isomorphism

Abstract

Two m × n matrices with ± 1 entries are Hadamard equivalent if one may be obtained from the other by a sequence of operations involving independent row and column permutations and multiplications of rows or columns by -1. We solve the computational problem of recognising Hadamard equivalence by reducing it to the problem of determining an isomorphism between two graphs with 2(m + n) vertices. Existing graph isomorphism algorithms permit the practical determination of Hadamard equivalence when m and n are of the order of several hundred. © 1979.