Simultaneously normalizable matrices
type: Item
instance of: scholarly article
title: Simultaneously normalizable matrices
zbMATH Open document ID: 0622.15004
DOI: 10.1016/0024-3795(87)90083-8
author: Christian Pommer
author: Wolfhard Kliem
published in: Linear Algebra and its Applications
publication date: 1987-01-01T00:00:00Z
review text: If \(A,B\in C^{n\times n}\), and there exists a nonsingular matrix W such that both \(W^{-1}AW\) and \(W^{-1}BW\) are normal, then A and B are said to be simultaneously normalizable. In this paper the author develops a necessary and sufficient condition for two matrices A and B to be simultaneously normalizable. This condition is expressed by the properties of the modal matrices (eigenvector matrices) of A and B. In addition, an application is demonstrated in the special case of simultaneously real symmetrizable matrices including geometrical interpretations, and a numerical example is given.
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 4008573
zbMATH Keywords: canonical form
zbMATH Keywords: simultaneously normalizable matrices
zbMATH Keywords: numerical example
reviewed by: Tong Wenting
MaRDI profile type: Publication
full work available at URL: 0024-3795(87)90083-8
OpenAlex ID: W2090002237
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description: scientific article; zbMATH DE number 4008573