A new class of spectrally arbitrary complex sign pattern

Abstract

Assume that S is an nth-order complex sign pattern. If for every nth degree complex coefficient polynomial f(λ) with a leading coefficient of 1, there exists a complex matrix C\in Q\left(S\right) such that the characteristic polynomial of C is f(λ), then S is called a spectrally arbitrary complex sign pattern. That is, if the spectrum of nth-order complex sign pattern S is a set comprised of all spectra of nth-order complex matrices, then S is called a spectrally arbitrary complex sign pattern. This paper presents a class of spectrally arbitrary complex sign pattern with only 3n nonzero elements by adopting the method of Schur complement and row reduction.

Keywords

Complex sign pattern / potentially nilpotent / spectrally arbitrary

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