Two New Classes of Spectrally Arbitrary Sign Patterns

Abstract

An \(n \times n\) sign pattern \(A\) is a spectrally arbitrary pattern if for any given real monic polynomial \(f(x)\) of degree \(n\), there is a real matrix \(B \in Q(A)\) having characteristic polynomial \(f(x)\). In this paper, we give two new classes of \(n \times n\) spectrally arbitrary sign patterns which are generalizations of the pattern \(W_{n}(k)\) defined in [T. Britz, J.J. McDonald, D.D. Olesky, P. van den Driessche, Minimal spectrally arbitrary sign patterns, SIAM Journal on Matrix Analysis and Applications, \(26(2004), 257-271]\).