The Maximal Determinant and Subdeterminants of ±1 Matrices

J. Seberry, University of Wollongong
T. Xia, University of Wollongong
C. Koukouvinos, National Technical University of Athens, Greece
M. Mitrouli, University of Athens, Greece

Article comments

This article was originally published as Seberry, J, Xia, T, Koukouvinos, C and Mitrouli, M, The Maximal Determinant and Subdeterminants of ±1 Matrices, Linear Algebra and Applications, 373, 2003, 297-310. Original Elsevier journal available here.

Abstract

In this paper we study the maximal absolute values of determinants and subdeterminants of ±1 matrices, especially Hadamard matrices. It is conjectured that the determinants of ±1 matrices of order n can have only the values k • p, where p is specified from an appropriate procedure. This conjecture is verified for small values of n. The question of what principal minors can occur in a completely pivoted ±1 matrix is also studied. An algorithm to compute the (n — j) x (n — j), j = 1, 2, ... minors of Hadamard matrices of order n is presented, and these minors are determined for j =1,...,4.