The real linear eigenvalue problem in \(\mathbb C^n\)
type: Item
instance of: scholarly article
title: The real linear eigenvalue problem in \(\mathbb C^n\)
zbMATH Open document ID: 1070.15006
author: Marko Huhtanen
author: Jan von Pfaler
published in: Linear Algebra and its Applications
publication date: 2005-02-23T00:00:00Z
review text: A real linear operator \({\mathcal M}\) acts on \(\mathcal{C}^n\) according to \(z\rightarrow {\mathcal M}z=Mz+M_{\#}\bar{z}\) for a pair of matrices \(M,M_{\#} \in \mathcal{C}^{n\times n}\) called the linear and antilinear parts of \({\mathcal M}.\) If \({\mathcal M}_{\#}=0\) (resp. \({\mathcal M}=0\)) then \({\mathcal M}\) is called \(\mathcal{C}\)-linear (resp. antilinear). The spectrum of \({\mathcal M}\) consists of those points \(\lambda \in \mathcal{C}\) for which \(\lambda I-{\mathcal M}\) is not invertible giving rise to a bounded, possibly empty, real algebraic plane curve of degree \(2n.\) The authors presents results concerning the location of the eigenvalues of \({\mathcal M}\) and classify components of the spectrum. Path continuation techniques are implemented for computing components and subsets of the spectrum once an eigenvalue is available. Three numerical examples illustrating the aspect studied have been presented.
reviewed by: Jaspal Singh Aujla
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A04
Mathematics Subject Classification ID: 14Q05
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 2137778
zbMATH Keywords: real linear operator
zbMATH Keywords: spectrum
zbMATH Keywords: characteristic bivariate polynomial
zbMATH Keywords: path following techniques
zbMATH Keywords: real algebraic plane curve
zbMATH Keywords: location of eigenvalues
zbMATH Keywords: numerical examples
describes a project that uses: JDQR
describes a project that uses: Matlab
describes a project that uses: JDQZ
MaRDI profile type: Publication
full work available at URL: j.laa.2004.07.004
OpenAlex ID: W2014466204
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DOI: 10.1016/J.LAA.2004.07.004
description: scientific article; zbMATH DE number 2137778