SPECTRA AND INVERSE SIGN PATTERNS OF NEARLY SIGN-NONSINGULAR MATRICES

A nearly sign-nonsingular (NSNS) matrix is a real n x n matrix having at least two nonzero terms in the expansion of its determinant with pr ecisely one of these terms having opposite sign to all the other terms . Using graph-theoretic techniques, we study the spectra of irreducibl e NSNS matrices in normal form. Specifically, we show that such a matr ix can have at most one nonnegative eigenvalue, and can have no nonrea l eigenvalue z in the sector (z:\arg z\ less than or equal to pi/(n -1 )). We also derive results concerning the sign pattern of inverses of these matrices. (C) Elsevier Science Inc., 1996