On integer matrices obeying certain matrix equations

Authors

Jennifer Seberry, University of WollongongFollow

Publication Details

Jennifer Seberry Wallis, On integer matrices obeying certain matrix equations, Journal of Combinatorial Theory, Ser. A., 12, (1972), 112-118.

Abstract

We discuss integer matrices B of odd order v which satisfy

Br = ± B, BBr = vI - J, BJ = O.

Matrices of this kind which have zero diagonal and other elements ± 1 give rise to skew-Hadamard and n-type matrices; we show that the existence of a skew-Hadamard (n-type) matrix of order h implies the existence of skew-Hadamard (n-type) matrices of orders (h - 1)⁵ + 1 and (h - 1)⁷ + 1. Finally we show that, although there are matrices B with elements other than ± 1 and 0, the equations force considerable restrictions on the elements of B.