SOME SIGN PATTERNS THAT ALLOW A REAL INVERSE PAIR B AND B-1

A sign pattern matrix is a matrix whose entries are from the set {+,-, 0}. For a real matrix B, by sgn B we mean the sign pattern matrix in w hich each positive (negative, zero) entry is replaced by + (-,0). If A is an n-by-n sign pattern matrix, then the sign pattern class of A is defined by Q(A) = {B is an element of M(n)(R)\sgn B = A}. Our purpose here is to investigate patterns that allow some B and B-1 to be in Q( A). To this end, we establish global necessary conditions, we obtain n ecessary and sufficient conditions for certain classes of patterns, an d we provide several construction algorithms to obtain classes of patt erns that have the inverse pair property. (C) Elsevier Science Inc., 1 997