On algebras of Toeplitz plus Hankel matrices
type: Item
instance of: scholarly article
title: On algebras of Toeplitz plus Hankel matrices
zbMATH Open document ID: 0839.15008
DOI: 10.1016/0024-3795(94)00299-S
author: Roberto Bevilacqua
author: Nazzareno Bonanni
author: Enrico Bozzo
published in: Linear Algebra and its Applications
publication date: 1995-07-24T00:00:00Z
review text: Let \({\mathcal K}\) be the space of all \(n \times n\) matrices which are the sum of a Toeplitz and a Hankel matrix. The authors use properties of displacement operators to give a nice proof that \(A \in {\mathcal K}\) if and only if \(A\) satisfies the cross-sum condition \[ a_{i - 1,j} + a_{i + 1,j} = a_{i,j - 1} + a_{i,j + 1} \quad \text{for all } i,j = 2, \dots, n - 1 \] and to characterize a wide class of maximal algebras in \({\mathcal K}\).
Mathematics Subject Classification ID: 15A30
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 778251
zbMATH Keywords: Toeplitz plus Hankel matrices
zbMATH Keywords: displacement operators
zbMATH Keywords: cross-sum condition
zbMATH Keywords: maximal algebras
MaRDI profile type: Publication
cites work: Fast parallel and sequential computations and spectral properties concerning band Toeplitz matrices
cites work: Spectral and computational properties of band symmetric Toeplitz matrices
cites work: Improved parallel computations with Toeplitz-like and Hankel-like matrices
cites work: Algebras of higher dimension for displacement decompositions and computations with Toeplitz plus Hankel matrices
cites work: On the Use of Certain Matrix Algebras Associated with Discrete Trigonometric Transforms in Matrix Displacement Decomposition
cites work: Q3208805
cites work: Analysis of Preconditioning Techniques for Ill-Conditioned Toeplitz Matrices
cites work: Matrix decompositions using displacement rank and classes of commutative matrix algebras
cites work: Displacement operator based decompositions of matrices using circulants or other group matrices
cites work: Inversion of Persymmetric Matrices Having Toeplitz Inverses
cites work: Displacement ranks of matrices and linear equations
cites work: Preconditioned Iterative Methods for Solving Toeplitz-Plus-Hankel Systems
cites work: On algebras of Toeplitz matrices
cites work: Displacement operators relative to group matrices
cites work: Algebraic and computational properties of a set of (0,1) matrices with prescribed sum
description: scientific article; zbMATH DE number 778251