一类含有3n个非零元的谱任意ray模式  

A Class of Spectrally Arbitrary Ray Patterns with 3n Nonzero Entries

作　　者：霍英杰[1] 乔晓玲[1] 邵燕灵[1] HUO Ying-jie QIAO Xiao-ling SHAO Yan-ling(School of Science, North University of China, Taiyuan 030051, China)

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《中北大学学报（自然科学版）》2017年第2期114-118,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11071227);山西省回国留学人员科研资助项目(12-070)

摘　　要：利用矩阵特征值理论,研究了一类含有3n个非零元的n阶ray模式矩阵.在该ray模式矩阵的定性矩阵类中任取一个n阶复矩阵,求出该复矩阵的特征多项式,利用数学分析的方法,找到该复矩阵为幂零矩阵的条件,再运用幂零-雅可比方法,证明了该类ray模式矩阵及其任意母模式都是谱任意的.Using matrix eigenvalue theory, a class of n X n ray pattern matrices with 3n nonzero entries was studied. Take any n ×n complex matrix belonged to the qualitative matrix class of the above ray pat- tern. The characteristic polynomial of this complex matrix was obtained. By the method of mathematical analysis, we found the condition that this complex matrix is nilpotent. Finally, we verify that the ray patterns and all superpatterns are spectrally arbitrary by Nilpotent-Jacobian method.

关 键 词：幂零-雅可比 ray模式 谱任意 蕴含幂零 

分 类 号：O157.5[理学—数学]