The matrix equation \(XA-BX=R\) and its applications
type: Item
instance of: scholarly article
title: The matrix equation \(XA-BX=R\) and its applications
zbMATH Open document ID: 0656.15006
DOI: 10.1016/0024-3795(88)90200-5
author: Karabi Datta
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: The author considers the Sylvester equation \(XA-BX=R\) for X where A, B and R are \(n\times n\) complex matrices, and B is nonderogatory. The main theorem shows that if only the first n-1 rows of R are given, then there is at most one solution X with a specified first row, and the author characterizes the case where X is nonsingular. This result is used to construct symmetrizers and commuting matrices, to compute the number of common eigenvalues between A and B, and to reprove some results on symmetrizers, Bézoutians and inertia.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 4071107
zbMATH Keywords: matrix equation
zbMATH Keywords: Sylvester equation
zbMATH Keywords: symmetrizers
zbMATH Keywords: commuting matrices
zbMATH Keywords: common eigenvalues
zbMATH Keywords: Bézoutians
zbMATH Keywords: inertia
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90200-5
OpenAlex ID: W2077639960
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description: scientific article; zbMATH DE number 4071107