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∈Q(S)such that the characteristic polynomi...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∈Q(S)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.展开更多
文摘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∈Q(S)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.
