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 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.

DOI

10.1080/03081089508818426

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