The eigenproblem of a tridiagonal 2-Toeplitz matrix
type: Item
instance of: scholarly article
title: The eigenproblem of a tridiagonal 2-Toeplitz matrix
zbMATH Open document ID: 0833.15009
DOI: 10.1016/0024-3795(94)90481-2
author: M. J. C. Gover
published in: Linear Algebra and its Applications
publication date: 1996-03-18T00:00:00Z
review text: A solution of the eigenproblem for a tridiagonal 2-Toeplitz matrix is presented. It is shown that the characteristic polynomial for the case \(r = 2\) of a generalized \(r\)-Toeplitz matrix possesses similar properties as the Chebyshev polynomial of the first kind. When the order of the matrix is odd then the eigenvalues can be found explicitly. The case of matrices with even order is not handled straightforwardly by means of Chebyshev zeroes. A formula for explicit calculation of eigenvectors of 2-Toeplitz matrices is presented.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 553953
zbMATH Keywords: tridiagonal 2-Toeplitz matrix
zbMATH Keywords: Chebyshev polynomial
zbMATH Keywords: eigenvalues
zbMATH Keywords: eigenvectors
reviewed by: Marián Vajteršic
MaRDI profile type: Publication
full work available at URL: 0024-3795(94)90481-2
OpenAlex ID: W1977528605
cites work: Q3661894
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cites work: Q3813193
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cites work: Q5591853
cites work: Algorithm 694
description: scientific article; zbMATH DE number 553953