Some thoughts on Gerstenhaber's theorem

被引:8
作者
Holbrook, J.
O'Meara, K. C.
机构
基金
加拿大自然科学与工程研究理事会;
关键词
Commutative matrix algebras; Irreducible matrix varieties; COMMUTING TRIPLES; VARIETIES; MATRICES; PAIRS; SUBALGEBRAS;
D O I
10.1016/j.laa.2014.10.009
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We weigh the current evidence for and against an extension of Gerstenhaber's 1961 theorem to three commuting matrices over a field. (C) 2014 Elsevier Inc. All rights reserved.
引用
收藏
页码:267 / 295
页数:29
相关论文
共 23 条
[1]  
Barria J., 1990, LINEAR MULTILINEAR A, V27, P147
[2]  
Bergman G.M., 2013, PREPRINT
[3]   ON DOMINANCE AND VARIETIES OF COMMUTING MATRICES [J].
GERSTENHABER, M .
ANNALS OF MATHEMATICS, 1961, 73 (02) :324-&
[4]   Commuting pairs and triples of matrices and related varieties [J].
Guralnick, RM ;
Sethuraman, BA .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 310 (1-3) :139-148
[5]  
Guralnick Robert M., 1992, Linear Multilinear Algebra, V31, P71
[6]  
Han YH, 2005, ELECTRON J LINEAR AL, V13, P274
[7]   Approximating commuting operators [J].
Holbrook, J ;
Omladic, M .
LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 327 (1-3) :131-149
[8]   POLYNOMIALS IN A MATRIX AND ITS COMMUTANT [J].
HOLBROOK, JAR .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1982, 48 (DEC) :293-301
[9]  
Horn R. A., 2013, Matrix Analysis, VSecond
[10]   2 GENERATED COMMUTATIVE MATRIX SUBALGEBRAS [J].
LAFFEY, TJ ;
LAZARUS, S .
LINEAR ALGEBRA AND ITS APPLICATIONS, 1991, 147 :249-273