摘要
以符号集合{+,-,0}中的元素构成的矩阵A称为符号模式矩阵或符号模式.如果对于符号模式A,实矩阵A中的元素与A中对应元素的符号相同,则称A是A的一个实现.如果A有一个实现是幂零矩阵,则称A为蕴含幂零的符号模式.该文引入了一类符号模式矩阵,记为FSP(3,n-3).得出FSP(3,n-3)中所有偶数阶的模式都不是蕴含幂零的,并且给出了n=7阶这种形式的符号模式蕴含幂零的充要条件.
A matrix A whose entries come from the set {+,-,0} is called a sign pattern matrix, or sign pattern. If A is a sign pattern and A is a real matrix for which each entry has the same sign as the corresponding entry of A, then A is said to be a realization of A. A sign pattern is said to be potentially nilpotent if it has a nilpotent realization. In this paper, a class of sign patterns, denoted by FSP(3, n - 3), is introduced. The authors determine all potentially nilpotent sign patterns in FSP(3, 4), and prove that no sign pattern of even order in FSP(3, n - 3) is Dotentially nilDotent.
出处
《数学物理学报(A辑)》
CSCD
北大核心
2011年第3期628-635,共8页
Acta Mathematica Scientia
基金
国家自然科学基金(11026143)
江西省教育厅青年科学基金(GJJ09460)
江西师范大学青年成长基金(2711)和江西师范大学科研博士启动基金(Grant2058)资助
关键词
符号模式矩阵
蕴含幂零
谱任意
Sign pattern matrix
Potentially nilpotent
Spectrally arbitrary.