The \(\psi_S\) polar decomposition
type: Item
instance of: scholarly article
title: The \(\psi_S\) polar decomposition
zbMATH Open document ID: 1176.15016
author: Roger A. Horn
author: Dennis I. Merino
author: Agnes T. Paras
published in: Linear Algebra and its Applications
publication date: 2009-09-10T00:00:00Z
review text: Let \(S\) be a nonsingular \(n\) by \(n\) complex matrix. The authors define \(\psi_S(A)\) for \(A\) being nonsingular and singular, respectively. It is proved that every nonsingular \(A\) has a \(\psi_S\) polar decomposition \(A=RE\), where \(R\) is \(\psi_S\) orthogonal and \(E\) is \(\psi_S\) symmetric. The authors also determine which singular matrices have a \(\psi_S\) polar decomposition.
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15B10
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 5602608
zbMATH Keywords: \(\psi_S\) polar decomposition
zbMATH Keywords: \(\psi_S\) orthogonal matrices
zbMATH Keywords: \(\psi_S\) symmetric matrices
zbMATH Keywords: \(\psi_S\) antiorthogonal matrices
zbMATH Keywords: coninvolutory matrices
zbMATH Keywords: skew-coninvolutory matrices
reviewed by: Chen Sheng
MaRDI profile type: Publication
full work available at URL: j.laa.2009.04.021
OpenAlex ID: W2057765807
cites work: Skew-coninvolutory matrices
cites work: Matrix Analysis
cites work: Q4040931
cites work: A real-coninvolutory analog of the polar decomposition
cites work: Contragredient equivalence: A canonical form and some applications
cites work: Quaternions and matrices of quaternions
DOI: 10.1016/J.LAA.2009.04.021
description: scientific article; zbMATH DE number 5602608