符号模式集FSP(3, n-3)中蕴含幂零的模式类

数学物理学报 ›› 2011, Vol. 31 ›› Issue (3): 628-635.

符号模式集FSP(3, n-3)中蕴含幂零的模式类

李红海¹|李炯生²|苏莉¹

1.江西师范大学 |数信学院南昌 330022|2.中国科学技术大学数学系合肥 230026

收稿日期:2009-07-08 修回日期:2010-08-05 出版日期:2011-06-25 发布日期:2011-06-25
基金资助:
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(Grant 2058)资助

The Potentially Nilpotent Sign Patterns in the Set of Sign Patterns FSP(3, n-3)

LI Hong-Hai¹, LI Jiong-Sheng², SU Li¹

1.College of Mathematic and Information Science, |Jiangxi Normal University, Nanchang 330022; 2.Department of Mathematics, |University of Science and Technology of China, Hefei |230026

Received:2009-07-08 Revised:2010-08-05 Online:2011-06-25 Published:2011-06-25
Supported by:
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(Grant 2058)资助

摘要/Abstract

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.

关键词: 符号模式矩阵, 蕴含幂零, 谱任意

Abstract:

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 potentially nilpotent.

Key words: Sign pattern matrix, Potentially nilpotent, Spectrally arbitrary

中图分类号:

05C50

李红海, 李炯生, 苏莉. 符号模式集FSP(3, n-3)中蕴含幂零的模式类[J]. 数学物理学报, 2011, 31(3): 628-635.

LI Hong-Hai, LI Jiong-Sheng, SU Li. The Potentially Nilpotent Sign Patterns in the Set of Sign Patterns FSP(3, n-3)[J]. Acta mathematica scientia,Series A, 2011, 31(3): 628-635.