Words and normality of matrices

Citation data:

Linear and Multilinear Algebra, ISSN: 0308-1087, Vol: 40, Issue: 2, Page: 111-118

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https://nsuworks.nova.edu/math_facarticles/133; https://works.bepress.com/fuzhen-zhang/9
Wang, Bo-Ying; Zhang, Fuzhen
Informa UK Limited; NSUWorks
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.