两类极小谱任意符号模式矩阵

Two classes spectrally arbitrary patterns matrixs

设A为n阶符号模式,对任意n次首1实系数多项式r(x),都能在符号模式A的定性矩阵类Q(A)中找到一个实矩阵B,使得B的特征多项式fB(x)=r(x),则称A是谱任意的.如果谱任意模A的任意一个真子模式都不是谱任意的,则称A为极小谱任意的.本文运用Nilpotent-Jacobian方法证明了两类含有2n+1个非零元的n阶(n≥6)符号模式是极小谱任意模式.

An n×n sign pattern A is spectrally arbitrary if every monic real polynomial of degree n can be achieved as the characteristic polynomial of some matrix B∈Q(A).If A is spectrally arbitrary,and no proper subpattern of A is spectrally arbitrary,then A is a minimal spectrally arbitrary sign pattern.In this paper,Two Classes Minimally spectrally arbitrary sign patterns Matrixs of order n with 2n+1 nonzero entries are given by using the Nilpotent-Jacobian method.