Complex spectrally arbitrary zero-nonzero patterns

被引：6
|
作者：
McDonald, J. J. [1 ]
Yielding, A. A. [2 ]
机构：
[1] Washington State Univ, Dept Math, Pullman, WA 99164 USA
[2] Eastern Oregon Univ, Dept Math, La Grande, OR 97850 USA
来源：
LINEAR & MULTILINEAR ALGEBRA | 2012年 / 60卷 / 01期
关键词：
spectrally arbitrary; zero-nonzero patterns; complex matrices; SIGN PATTERNS; MATRICES; ORDER-4;
D O I：
10.1080/03081087.2010.512730
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this article, we highlight interesting properties of complex spectrally arbitrary zero-nonzero patterns. In particular, we investigate irreducible complex spectrally arbitrary zero-nonzero patterns for which all Jacobians are zero at every nilpotent realization. We also study complex spectrally arbitrary patterns whose corresponding directed graph does not contain a two-cycle. Lastly, we provide a complete list of all 3 x 3 and 4 x 4 complex spectrally arbitrary zero-nonzero patterns.
引用
收藏
页码：11 / 26
页数：16
相关论文
共 50 条
  • [1] REFINED INERTIALLY AND SPECTRALLY ARBITRARY ZERO-NONZERO PATTERNS
    Deaett, L.
    Olesky, D. D.
    van den Driessche, P.
    ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2010, 20 : 449 - 467
  • [2] Spectrally arbitrary zero-nonzero patterns and field extensions
    McDonald, Judith J.
    Melvin, Timothy C.
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 519 : 146 - 155
  • [3] Spectrally arbitrary zero-nonzero patterns of order 4
    Corpuz, L.
    McDonald, J. J.
    LINEAR & MULTILINEAR ALGEBRA, 2007, 55 (03): : 249 - 273
  • [4] Inertias of zero-nonzero patterns
    Kim, In-Jae
    McDonald, J. J.
    Olesky, D. D.
    Van Den Driessche, P.
    LINEAR & MULTILINEAR ALGEBRA, 2007, 55 (03): : 229 - 238
  • [5] Inverse invariant zero-nonzero patterns
    Ma, Chao
    Zhan, Xingzhi
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 443 : 184 - 190
  • [6] Integrally normalizable matrices and zero-nonzero patterns
    Garnett, C.
    Olesky, D. D.
    Shader, B. L.
    van den Driessche, P.
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 449 : 132 - 153
  • [7] Three remarks on spectra of zero-nonzero patterns
    Shitov, Yaroslav
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 534 : 73 - 77
  • [8] Zero-nonzero tree patterns that allow Sn*
    Gan, Luyining
    Gao, Wei
    Han, Jie
    LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (22): : 7347 - 7369
  • [9] Zero-Nonzero Matrices
    Stong, Richard
    AMERICAN MATHEMATICAL MONTHLY, 2012, 119 (06): : 526 - 526
  • [10] ZERO-NONZERO PATTERNS FOR NILPOTENT MATRICES OVER FINITE FIELDS
    Vander Meulen, Kevin N.
    Van Tuyl, Adam
    ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2009, 18 : 628 - 648
12345