两个新的极小谱任意符号模式
Two New Minimally Spectrally Arbitrary Sign Patterns
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摘要: 设A为n阶符号模式矩阵,若给定任意一个n次首一实系数多项式f(λ),都存在一个实矩阵B∈Q(A),使得B的特征多项式为f(λ),则称A为谱任意符号模式.如果一个谱任意符号模式中的一个或多个非零元被零取代后所得到的符号模式不是谱任意的,则称这个谱任意符号模式为极小谱任意的.文中证明了两个新的符号模式是极小谱任意的.Abstract: A spectrally arbitrary pattern A of order n is a sign pattern such that every monic real polynomial of degree n can be achieved as the characteristic polynomial of a matrix with sign pattern A.A sign pattern A is minimally spectrally arbitrary if it is spectrally arbitrary but there is not proper subpattern of A which is spectrally arbitrary.In this paper,two new sign patterns which are minimally spectrally arbitrary are proved by the Nilpotent-Jacobian method.