Multi-companion matrices
type: Item
instance of: scholarly article
published in: Linear Algebra and its Applications
volume: 354
issue: 1-3
page(s): 53-83
publication date: 2002-10-01T00:00:00Z
publication date: 2003-02-05T00:00:00Z
author: Georgi N. Boshnakov
title: Multi-companion matrices
zbMATH Open document ID: 1016.15006
review text: Multi-companion matrices are defined, characterized, and studied. They generalize companion matrices. Generalized eigenvectors of multi-companion matrices are described and parametrized by their eigenvalues. It is found that each (generalized) eigenvector of a \(k\)-companion \(m\times m\) matrix can be represented as a simple function of the corresponding eigenvalue and \(k-1\) quantities, which are functionally independent from all eigenvalues of the matrix and the generalized eigenvectors corresponding to different eigenvalues. An application in periodic autoregression and in multivariate autoregression in continuous time is described.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62J12
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 1864715
zbMATH Keywords: multi-companion matrices
zbMATH Keywords: Jordan decomposition
zbMATH Keywords: continuous-time autoregression
zbMATH Keywords: generalized eigenvectors
zbMATH Keywords: eigenvalues
describes a project that uses: partsm
MaRDI profile type: Publication
cites work: Q3994675
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cites work: Inertia characteristics of self-adjoint matrix polynomials
DOI: 10.1016/S0024-3795(01)00475-X
description: scientific article; zbMATH DE number 1864715