一类含有3n个非零元的谱任意ray模式

Class of Spectrally Arbitrary ray Patterns with 3n Nonzero Entries

若对任意n次首一复系数多项式f(λ),都存在复矩阵A∈Q(P),使得A的特征多项式为f(λ),则称ray模式矩阵P为谱任意的。本文利用幂零-雅克比方法证明了一类含有3n个非零元的n阶ray模式及其母模式为谱任意的。

A ray pattern P is spectrally arbitrary if given any monic polynomial f（λ） of order n with complex coefficients,and there exists A∈Q（P）,thus the characteristic polynomial of A is f（λ）.A class ray pattern of order n matrix with nonzero entries was presented.It is show that this ray pattern and its superpattern are spectrally arbitrary by nilpotent-Jacobi method.