On the number of invariant factors of matrix products

被引：0

作者：

de Sá, EM

Zhang, YL

机构：

[1] Univ Coimbra, Dept Matemat, P-3000 Coimbra, Portugal

[2] Univ Minho, Dept Matemat, P-4710 Braga, Portugal

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2005年 / 401卷

关键词：

nilpotent matrices; invariant factors; similarity;

D O I：

10.1016/j.laa.2004.10.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove an inequality relating the number of nontrivial invariant factors of n x it matrices A and B, with those of AB, and get some results on the cases of equality. In particular, we characterize the similarity classes, 4 and 2, with all eigenvalues in the base field, such that AB is nilpotent for some A epsilon A and B epsilon B. (c) 2004 Elsevier Inc. All rights reserved.

引用

页码：393 / 399

页数：7

共 9 条

[1] [Anonymous], LINEAR MULTILINEAR A
[2] Products of matrices with prescribed spectra and ranks
Furtado, S
Iglésias, L
Silva, FC
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 340 (340) : 137 - 147
[3] Lin ZY, 1998, LINEAR ALGEBRA APPL, V277, P253
[4] SA EMD, 1979, LINEAR ALGEBRA APPL, V24, P33, DOI 10.1016/0024-3795(79)90145-9
[5] Silva F. C., 1990, LINEAR MULTILINEAR A, V27, P317
[6] Sourour A. R., 1986, Linear Multilinear Algebra, V19, P141
[7] FACTORIZATION OF SINGULAR MATRICES
SOUROUR, AR
TANG, K
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 116 (03) : 629 - 634
[8] INTERLACING INEQUALITIES FOR INVARIANT FACTORS
THOMPSON, RC
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1979, 24 (APR) : 1 - 31
[9] WU PY, 1987, LINEAR ALGEBRA APPL, V96, P227

← 1 →