Lyapunov, Bézout, and Hankel
type: Item
instance of: scholarly article
title: Lyapunov, Bézout, and Hankel
zbMATH Open document ID: 0567.15008
DOI: 10.1016/0024-3795(84)90220-9
author: Vlastimil Pták
published in: Linear Algebra and its Applications
publication date: 1984-01-01T00:00:00Z
review text: Given a polynomial f of degree n, we denote by C its companion matrix, and by S the truncated shift operator of order n. We consider Lyapunov- type equations of the form \(X-SXC=W\) and \(X-CXS=W.\) We derive some properties of these equations which make it possible to characterize Bezoutian matrices as solutions of the first equation with suitable right-hand sides W (similarly for Hankel and the second equation) and to write down explicit expressions for these solutions. This yields explicit factorization formulae for polynomials in C, for the Schur-Cohn matrix, and for matrices satisfying certain intertwining relations, as well as for Bezoutian matrices.
Mathematics Subject Classification ID: 15A24
Mathematics Subject Classification ID: 93D05
zbMATH DE Number: 3904764
zbMATH Keywords: Hankel matrix
zbMATH Keywords: matrix equations
zbMATH Keywords: companion matrix
zbMATH Keywords: truncated shift operator
zbMATH Keywords: Lyapunov-type equations
zbMATH Keywords: Bezoutian matrices
zbMATH Keywords: factorization
zbMATH Keywords: Schur-Cohn matrix
MaRDI profile type: Publication
full work available at URL: 0024-3795(84)90220-9
OpenAlex ID: W1973131596
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description: scientific article; zbMATH DE number 3904764