## Mathematics Faculty Articles

#### Title

Words and Normality of Matrices

#### 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 *A ^{2} *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.

http://nsuworks.nova.edu/math_facarticles/133

#### DOI

10.1080/03081089508818426