一类含有2n个非零元的极小谱任意符号模式

摘要

一个n × n符号模式A是谱任意的,如果对任给的n阶首一实系数多项式 f (x),都存在实矩阵B∈Q(A),且其特征多项式为 f (x)。如果符号模式A是谱任意的,且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。本文给出了一类新的含有2n个非零元的符号模式A,运用 Nilpotent-Jacobian方法证明了n阶(n≥7)符号模式A是极小谱任意模式。%An n × n sign pattern A is said to be spectrally arbitrary if for each monic real polynomial f(x) of degree n there exists a matrix B is in Q (A) that has f(x) as its characteristic polynomial. If A is spectrally arbitrary, and no proper subpattern of A is spectrally arbitrary, then A is a minimal spectrally arbitrary sign pattern. A new class of sign patterns A with 2n nonzero entries is given. It is proved that n × n (n≥7) sign pattern A is a minimal spectrally arbitrary pattern by using the Nilpotent-Jacobian method.