Some Spectrally and Inertially Arbitrary Sign Patterns

梅银珍; 王鹏; 陈淑琴

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Some Spectrally and Inertially Arbitrary Sign Patterns

更新时间：2026-09-14

- Some Spectrally and Inertially Arbitrary Sign Patterns
- 几类特殊的谱任意和惯量任意符号模式矩阵
- Vol. 30, Issue 4, Pages: 307-311(2009)
- 作者机构：
  
  中北大学理学院
- 作者简介：
- 基金信息：
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- Published：2009
- 稿件说明：
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梅银珍, 王鹏, 陈淑琴. Some Spectrally and Inertially Arbitrary Sign Patterns[J]. 2009, 30(4): 307-311.
DOI：

梅银珍, 王鹏, 陈淑琴. Some Spectrally and Inertially Arbitrary Sign Patterns[J]. 2009, 30(4): 307-311. DOI：

摘要

利用矩阵理论和组合论的方法对一些特殊类型的符号模式的惯量和谱进行了研究.找到了一类谱任意的零-非零符号模式矩阵

同时也是惯量任意的符号模式矩阵

证明了Hessenberg型矩阵对应的符号模式矩阵是极小惯量任意符号模式矩阵;给出一类由低阶矩阵通过直和构造而成的几乎完全惯量任意符号模式矩阵;通过对形如"S"的特殊符号模式矩阵的分析

利用矩阵分解的性质得到了谱任意符号模式矩阵的一个必要条件.

Abstract

By combinatorial and matrix theoretical methods

the study is focused on some special sign pattern matrices.A class of spectrally and inertially arbitrary zero-nonzero pattern is given.It is proved that the Hessenberg-matrix is the minimal inertially arbitrary sign pattern.An almost inertially arbitrary sign pattern that is constructed by the direct sum from those of lower order is introduced.Based on the property of matrix-decomposition for analyzing S-shaped sign pattern matrix

a necessary condition on the spectrally arbitrary sign pattern matrix is characterized.

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references

Drew J H,Olesky D D,Johnson C R,et al.Spectrally arbitrary patterns[J].Linear Algebra and its Applications,2000,308:121-137.

Cavers M S,Vander Meulen K N.Spectrally and inertially arbitrary sign patterns[J].Linear Algebra and itsApplications,2005,394:53-72.

Gao Yubin,Shao Yanling.Inertially arbitrary pattern[J].Linear and Maltilinear Algebra,2001,49:161-168.

Britz T,Mcdonald J J,Olesky D D,et al.Minimal spectrally arbitrary sign patterns[J].SIAM Journal on MatrixAnalysis and Applications,2004,26:257-271.

Miao Zhenke,Li Jiongsheng.Inertially arbitrary(2r-1)-diagonal sign patterns[J].Linear Algebra Algebra and itsApplications,2002,357:131-141.

Kim I J,Olesky D D,Driessche P V,et al.Inertially arbitrary sign patterns with no nilpotent realization[J].LinearAlgebra and its Applications,2007,421:264-283.

Hall F J,Li Zhongshan,Wang Di.Symmetric sign pattern matrices that require unique inertia[J].Linear Algebraand its Applications,2001,338:153-169.

DeAlba L M,Hentzel I R,Hogben L,et al.Spectrally arbitrary patterns:reducibility and the 2n-conjecture for n=5[J].Linear Algebra and its Applications,2007,423:262-276.

Cavers M S,Kim I J,Shader B L,et al.On determining minimal spectrally arbitrary patterns[J].Electron.J.Linear Algebra,2005,13:240-248.

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