一类恰含有3n个元的谱任意ray模式矩阵

A class of spectrally arbitrary ray patterns with 3n nonzero entries

研究一类n阶的恰含有3n个元的ray模式矩阵,证明该ray模式矩阵为蕴含幂零和谱任意的。给出该ray模式矩阵的定性矩阵类中一个n阶复矩阵,求出该复矩阵的特征多项式;由该特征多项式得出这类ray模式矩阵蕴含幂零,且其雅克比矩阵的行列式不为0。由McDonald和Stuart的幂零-雅克比方法,得出该ray模式矩阵及其母模式为谱任意的。

A class of n× n potential nilpotent and spectrally arbitrary ray pattern matrices with 3n nonzero entries is researched. Firstly, one of this ray patten matrix＇ s corresponding complex matrices is presented. The characteristic polynomial of this complex matrix is also obtained. From this characteristic polynomial, it can be obtained that this ray patten matrix is potential nilpotent and its Jacobian＇s determi-nant is nonzero. Finally, it is shown that this ray pattern matrix and all its superpatterns are spectrally ar- bitrary by McDonald and Stuart＇ s nilpotent-Jacobi method.