On the numerical ranges of matrix products
type: Item
instance of: scholarly article
title: On the numerical ranges of matrix products
zbMATH Open document ID: 1192.15009
author: Mao-Ting Chien
author: Chung-Lien Ko
author: Hiroshi Nakazato
published in: Applied Mathematics Letters
publication date: 2010-05-21T00:00:00Z
review text: Let \(M_n\) denote the space of complex \(n\times n\) matrices, and let~\(A,B,C\in M_n\). The \(C\)-numerical range of~\(A\) is defined by \(W_C(A)=\{\mathrm{tr}\,(CU^*AU):\,U\in M_n\, \mathrm{is\,unitary}\}\). The authors study the equation (1)~\(W_C(AB)=W_C(BA)\). First, they prove this if \(A\) and \(B\) are symmetric and \(C\) is normal. Second, they discuss the cases \(n=2\) and \(n=3\). Finally, they show that (1) holds if \(C\) is normal and \(A\) and \(B\) are Toeplitz matrices or matrices symmetric with respect to their backward diagonals or continuant matrices (i.e., tridiagonal matrices with entries \(1\) in the first diagonal above the main diagonal and \(-1\) in the first diagonal below it).
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15B05
Mathematics Subject Classification ID: 15A27
zbMATH DE Number: 5710922
zbMATH Keywords: numerical ranges
zbMATH Keywords: Toeplitz matrices
zbMATH Keywords: continuant matrices
zbMATH Keywords: commutativity
reviewed by: Jorma K. Merikoski
MaRDI profile type: Publication
full work available at URL: j.aml.2010.02.019
OpenAlex ID: W1994603611
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DOI: 10.1016/J.AML.2010.02.019
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description: scientific article; zbMATH DE number 5710922