Unitarily achievable zero patterns and traces of words in \(A\) and \(A\)
type: Item
instance of: scholarly article
title: Unitarily achievable zero patterns and traces of words in \(A\) and \(A\)
zbMATH Open document ID: 1122.15014
author: Charles R. Johnson
author: Dragomir Ž. Đoković
published in: Linear Algebra and its Applications
publication date: 2007-02-12T00:00:00Z
review text: As a main objective, the authors investigate the problem of which patterns of zeros are achievable in matrices via unitary similarity of complex square matrices. A further objective is to bring to the attention of the linear algebra community some recent advances concerning the old problem of unitary similarity of two complex \(n\times n\) matrices \(A\) and \(B\). A theorem due to \textit{W. Specht} [Jahresber. Dtsch. Math.-Ver. 50, Abt. 1, 19--23 (1940; Zbl 0023.00203)] gives the N\&S condition: \(\text{tr}(w(A,A^*))= \text{tr}(w(B,B^*))\) for all words \(w\) in two non-commuting variables. This was later improved in that the condition need only hold for all words of length at most \(2n^2\) or even \(n^2\).
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 03D40
zbMATH DE Number: 5123957
zbMATH Keywords: unitary similarity
zbMATH Keywords: Schur's triangularization theorem
zbMATH Keywords: Specht's criterion for unitary similarity
reviewed by: Rabe von Randow
MaRDI profile type: Publication
full work available at URL: j.laa.2006.03.002
OpenAlex ID: W1979340931
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DOI: 10.1016/J.LAA.2006.03.002
description: scientific article; zbMATH DE number 5123957