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, $26(2004),257-271]$.