Centrosymmetric and centro-skewsymmetric Toeplitz-plus-Hankel matrices and Bézoutians
type: Item
instance of: scholarly article
title: Centrosymmetric and centro-skewsymmetric Toeplitz-plus-Hankel matrices and Bézoutians
zbMATH Open document ID: 1031.15025
DOI: 10.1016/S0024-3795(02)00506-2
author: G. Heinig
author: Karla Rost
published in: Linear Algebra and its Applications
publication date: 2003-05-25T00:00:00Z
review text: The present paper can be seen as a continuation of the authors' paper [ibid. 343-344, 195-209 (2002; Zbl 0995.15022)]. However, now Toeplitz matrices which are at the same time Hankel (shortly: T + H matrices) are considered, and for centrosymmetric [centro-skewsymmetric] matrices of this type algebraic properties are investigated. One of the main results is concerned with the inversion of regular centrosymmetric [centro-skewsymmetric] T + H matrices. The inverse of such a matrix can be represented with the help of some special, simply structured T + H Bézoutian. For singular matrices of this kind the structure of the kernel is described in terms of the related Toeplitz system. Furthermore, centrosymmetric [centro-skewsymmetric] T + H Bézoutians are characterized: General centrosymmetric [centro-skewsymmetric] T + H Bézoutians can be represented as the sum of two special T + H Bézoutians which can be reduced to Hankel Bézoutians of about half their size.
reviewed by: Hans Havlicek
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 1915808
zbMATH Keywords: Toeplitz-plus-Hankel matrix
zbMATH Keywords: Bézoutian
zbMATH Keywords: centrosymmetric matrix
zbMATH Keywords: matrix inversion
MaRDI profile type: Publication
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full work available at URL: s0024-3795(02)00506-2
OpenAlex ID: W2090990587
description: scientific article; zbMATH DE number 1915808