Required nonzero patterns for nonsingular sign regular matrices

Abstract

An n × n real matrix is called sign regular if, for each k ( 1 ⩽ k ⩽ n ) , all its minors of order k have the same nonstrict sign. The zero entries which can appear in a nonsingular sign regular matrix depend on its signature because the signature can imply that certain entries are necessarily nonzero. The patterns for the required nonzero entries of nonsingular sign regular matrices are analyzed.