Nonsymmetric Toeplitz matrices that commute with tridiagonal matrices
type: Item
instance of: scholarly article
title: Nonsymmetric Toeplitz matrices that commute with tridiagonal matrices
zbMATH Open document ID: 0832.15006
DOI: 10.1007/BF02110375
published in: Mathematical Notes
publication date: 1995-09-25T00:00:00Z
review text: A description of nonsymmetric Toeplitz matrices which commute with an irreducible tridiagonal matrix is presented. If \({\mathcal T}_s\) denotes the set of symmetric Toeplitz \(n\times n\) matrices which commute with an irreducible tridiagonal matrix, then for the sets \({\mathcal T}\) and \({\mathcal T}_H\) of Toeplitz and Hermitian Toeplitz \(n\times n\) matrices, respectively, which commute with an irreducible tridiagonal matrix the formulas \(T\in {\mathcal T} \Rightarrow T= D_\varepsilon T_s D_\varepsilon^{-1}\) for some \(\varepsilon\neq 0\) and \(T_H\in {\mathcal T}\Rightarrow T= D_\varepsilon Q_s D_\varepsilon^{-1}\) for some \(\varepsilon\), \(|\varepsilon|=1\), where \(T_s, Q_s\in {\mathcal T}_s\) and \(D_\varepsilon= \text{diag} (1, \varepsilon, \varepsilon^2, \dots, \varepsilon^{n- 1})\), are derived. A complete description of the set \(T\) for \(n= 2, 3, 4\) closes this paper.
Mathematics Subject Classification ID: 15A27
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 797888
zbMATH Keywords: commutativity
zbMATH Keywords: nonsymmetric Toeplitz matrices
zbMATH Keywords: irreducible tridiagonal matrix
author: Kh. D. Ikramov
reviewed by: Jan Zítko
MaRDI profile type: Publication
cites work: Q3776480
cites work: Toeplitz matrices commuting with tridiagonal matrices
cites work: Q5599376
cites work: Computing the eigenvalues of skew-symmetric matrices
full work available at URL: https://doi.org/10.1007/bf02110375
OpenAlex ID: W2079527404
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description: scientific article; zbMATH DE number 797888