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.
McKay, B. D. (1979). Hadamard equivalence via graph isomorphism. Discrete Mathematics, 27(2), 213–214. https://doi.org/10.1016/0012-365X(79)90113-4