Words and Normality of Matrices

Authors

Bo-Ying Wang, Beijing Normal University
Fuzhen Zhang, Nova Southeastern UniversityFollow

Document Type

Article

Publication Date

1995

Publication Title

Linear and Multilinear Algebra

ISSN

0308-1087

Volume

40

Issue/No.

2

First Page

111

Last Page

118

Abstract

Let A’ denote the conjugate transpose of an n×n complex matrix A and let ^(A,A) be a word in A and A′ wilh length m The following are shown: 1.If ^{(A, A*)} or its cycle contains A² or (A *)² and if tr(A,A *)=tr(A * A) ^m/2 then A is a normalmatrix; 2.If the difference of the numbers of A's and A* 's in the word is k≠0, then tr

^{(A *)} = tr(A * A)^m/2 if and only if A ^k = (A *A) ^k/2. A number of consequences are also presented.

NSUWorks Citation

Wang, Bo-Ying and Zhang, Fuzhen, "Words and Normality of Matrices" (1995). Mathematics Faculty Articles. 133.
https://nsuworks.nova.edu/math_facarticles/133

DOI

10.1080/03081089508818426