Words and Normality of Matrices

Citation data:

Linear and Multilinear Algebra, ISSN: 1563-5139, Vol: 40, Issue: 2, Page: 111-118

Publication Year:
1995
Usage 5
Abstract Views 5
Citations 3
Citation Indexes 3
Repository URL:
https://nsuworks.nova.edu/math_facarticles/133; https://works.bepress.com/fuzhen-zhang/9
DOI:
10.1080/03081089508818426
Author(s):
Wang, Bo-Ying; Zhang, Fuzhen
Publisher(s):
Informa UK Limited; NSUWorks
Tags:
Mathematics
article description
Let A* denote the conjugate transpose of an n × n complex matrix. A and let M(A, A*) be a word in A and A* with length m The following are shown: 1. If W(A, A*) or its cycle contains Aor (A*)and if tr W(A, A*)=tr(A*,A)then A is a normal matrix; 2. If the difference of the numbers of A's and A*'s in the word is k ≠ 0, then tr W(A, A*)=tr(A*,A)if and only if A= (A*A). A number of consequences are also presented. © 1995, Taylor & Francis Group, LLC. All rights reserved.