Positive integer powers of certain tridiagonal matrices
type: Item
instance of: scholarly article
title: Positive integer powers of certain tridiagonal matrices
zbMATH Open document ID: 1149.15019
author: Jesús Gutiérrez-Gutiérrez
published in: Applied Mathematics and Computation
publication date: 2008-09-01T00:00:00Z
review text: The author presents an extension of previous works of \textit{J. Rimas} [Appl. Math. Comput. 168, No. 2, 783--787 (2005; Zbl 1082.65523), ibid. 171, No. 2, 1214--1217 (2005; Zbl 1090.65048)], where he derived a general expression for the entries of the \(q\)th power (\(q\in\mathbb {N}\)) of the \(n\times n\) real symmetric tridiagonal matrix \(\text{tridiag}_n(1,0,1)\) for all \(n\in\mathbb {N}\). He derives a similar expression for the entries of the \(q\)th power \((q\in\mathbb {N})\) of the \(n\times n\) Hermitian tridiagonal matrix \(\text{tridiag}_n(a_1,a_0,\overline{a_1})\).
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A21
zbMATH DE Number: 5318702
zbMATH Keywords: eigenvalues
zbMATH Keywords: eigenvectors
zbMATH Keywords: Jordan's form
zbMATH Keywords: Chebyshev polynomials
zbMATH Keywords: Hermitian tridiagonal matrix
reviewed by: Andreas Arvanitoyeorgos
MaRDI profile type: Publication
full work available at URL: j.amc.2008.01.022
OpenAlex ID: W2047219983
cites work: On computing of arbitrary positive integer powers for one type of symmetric tridiagonal matrices of even order. I
cites work: On computing of arbitrary positive integer powers for one type of symmetric tridiagonal matrices of odd order. I
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cites work: On computing of arbitrary positive integer powers for one type of even order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis. II
cites work: On computing of arbitrary positive integer powers for one type of odd order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis. I
cites work: On computing of arbitrary positive integer powers for one type of symmetric tridiagonal matrices of even order. II.
cites work: On computing of arbitrary positive integer powers for one type of symmetric tridiagonal matrices of odd order. II
cites work: On computing of arbitrary positive integer powers for one type of odd order skew-symmetric tridiagonal matrices with eigenvalues on imaginary axis. II.
cites work: On the eigenvalue problem for Toeplitz band matrices
DOI: 10.1016/J.AMC.2008.01.022
description: scientific article; zbMATH DE number 5318702