一类新的Ray谱任意符号模式  

A New Family of Ray Spectrally Arbitrary Patterns

作　　者：梅银珍[1] 高玉斌[1] 

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）》2016年第1期1-5,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);山西省留学基金资助项目(2012-070)

摘　　要：研究了组合矩阵论中Ray模式矩阵的谱任意及其极小化问题.首先利用推广的幂零-雅可比方法,通过矩阵和图之间的关系证明给定模式类矩阵的雅可比行列式是非零的;寻找给定Ray符号模式的一个幂零矩阵,从而得到了一类新的仅含3n个非零元的谱任意Ray-符号模式矩阵.然后利用矩阵分析的方法证明该模式也是极小Ray-谱任意符号模式.This paper discussed a class of minimal Ray spectrally arbitrary pattern Ray sign patterns. Firstly, by the extended nilpotent-Jacobi method, the relationship between the matrix and the corresponding graph was applied to prove that the determinant of the Jacobi matrix is nonzero in the given Ray pattern class,a nilpotent matrix was found in the given Ray pattern class, and a new family of spectrally arbitrary Ray patterns that have exactly 3n nonzeros was obtained. Secondly, by the matrix analy- sis theorem, the patterns are the minimal Ray spectrally arbitrary patterns were proved.

关 键 词：Ray-符号模式 幂零-雅可比方法 Ray-谱任意符号模式 极小Ray-谱任意符号模式 

分 类 号：O157.5[理学—数学]