A geometric construction for spectrally arbitrary sign pattern matrices and the 2n-conjecture

Abstract

We develop a geometric method for studying the spectral arbitrariness of a given sign pattern matrix. The method also provides a computational way of computing matrix realizations for a given characteristic polynomial. We also provide a partial answer to 2n-conjecture. We determine that the 2n-conjecture holds for the class of spectrally arbitrary patterns that have a column or row with at least n − 1 nonzero entries.