一个极小谱任意的复符号模式

A minimally spectrally arbitrary complex sign pattern

对于n×n复符号模式S,若给定任意一个n阶首1复系数多项式f()λ,都存在一个复矩阵B∈Q(S),使得它的特征多项式为f()λ,则称S是谱任意的.若S是谱任意的,且它的任意真子模式都不是谱任意的,那么S是极小谱任意的.本文用扩展了的幂零—雅可比方法证明一个复符号模式是极小谱任意的.

An n × n complex sign pattern S is a spectrally arbitrary pattern if given any monic polynomial f（λ） with coefficients from C of order n,there exists a complex sign pattern B in Q（ S） such that its characteristic polynomial is f（λ）. If S is a spectrally arbitrary,and no proper subpattern of S is spectally arbitrary,then S is a minimal spectrally arbitrary complex sign pattern. In this paper we use extended Nilpotent- Jacobian method to prove a complex sign pattern is minimally spectrally arbitrary.