Allow problems concerning spectral properties of sign pattern matrices: A survey

被引：30
作者：
Catral, M. [2 ]
Olesky, D. D. [1 ]
van den Driessche, P. [2 ]
机构：
[1] Univ Victoria, Dept Comp Sci, Victoria, BC V8W 3P6, Canada
[2] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2009年 / 430卷 / 11-12期
基金：
加拿大自然科学与工程研究理事会;
关键词：
Inertially arbitrary; Potentially nilpotent; Potentially stable; Signed digraph; Sign pattern matrix; Spectrally arbitrary; POTENTIALLY NILPOTENT; NONZERO PATTERNS; INERTIA SETS; STABILITY;
D O I：
10.1016/j.laa.2009.01.031
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An n x n sign pattern matrix has entries in {+, -. 0}. This paper surveys the following problems concerning spectral properties of sign pattern matrices: sign patterns that allow all possible spectra (spectrally arbitrary sign patterns): sign patterns that allow all inertias (inertially arbitrary sign patterns); sign patterns that allow nilpotency (potentially nilpotent sign patterns); and sign patterns that allow stability (potentially stable sign patterns). Relationships between these four classes of sign patterns are given, and several open problems are identified. (C) 2009 Elsevier Inc. Ail rights reserved.
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收藏
页码：3080 / 3094
页数：15
相关论文
共 62 条
[31]  
Gao YB, 2008, JP J ALGEBR NUMBER T, V11, P15
[32]  
Hall F., 2007, HDB LINEAR ALGEBRA
[33]  
Hall F.J., 2001, J. Chin. Univ., V10, P226
[34]   Symmetric sign pattern matrices that require unique inertia [J].
Hall, FJ ;
Li, ZS ;
Wang, D .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 338 (338) :153-169
[35]   SOME SIGN PATTERNS THAT PRECLUDE MATRIX STABILITY [J].
JEFFREIS, C ;
JOHNSON, CR .
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1988, 9 (01) :19-25
[36]   QUALITATIVE STABILITY OF LINEAR-SYSTEMS [J].
JEFFRIES, C ;
KLEE, V ;
VANDENDRIESSCHE, P .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1987, 87 :1-48
[37]   Nested sequences of principal minors and potential stability [J].
Johnson, CR ;
Maybee, JS ;
Olesky, DD ;
vandenDriessche, P .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1997, 262 :243-257
[38]   THE POTENTIALLY STABLE TREE SIGN PATTERNS FOR DIMENSIONS LESS THAN 5 [J].
JOHNSON, CR ;
SUMMERS, TA .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1989, 126 :1-13
[39]   COMBINATORIAL MATRIX ANALYSIS - AN OVERVIEW [J].
JOHNSON, CR .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1988, 107 :3-15
[40]   Computing the inertia from sign patterns [J].
Kakimura, Naonori ;
Iwata, Satoru .
MATHEMATICAL PROGRAMMING, 2007, 110 (01) :229-244
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