Eigenvalue contour lines of Kac-Murdock-Szegő matrices with a complex parameter
type: Item
instance of: scholarly article
title: Eigenvalue contour lines of Kac-Murdock-Szegő matrices with a complex parameter
zbMATH Open document ID: 1473.15032
author: George Fikioris
author: Christos Papapanos
published in: Linear Algebra and its Applications
publication date: 2021-09-02T00:00:00Z
full work available at URL: https://arxiv.org/abs/2104.11527
review text: This paper deals with the eigenvalues of the Toeplitz matrix \[K_n(\rho) =[\rho^{|j-k|}]_{j,k=1}^n=\left[\begin{array}{ccccc}1& \rho &\rho^2&\ldots &\rho^{n-1}\\ \rho &1 &\rho&\ldots &\rho^{n-2}\\ \rho^2& \rho& 1&\ldots &\rho^{n-3}\\ \vdots &\vdots &\vdots &\ddots &\vdots \\ \rho^{n-1}& \rho^{n-2} &\rho^{n-3}&\ldots &1\end{array}\right]\] with \(n\geq 3\) and \(\rho\in\mathbb{C}\). The main result is Theorem 4.1, that is proved using some specific properties of Chebyshev polynomials. Numerical results and illustrative examples support the theoretical findings.
reviewed by: Rosário Fernandes
Mathematics Subject Classification ID: 15B05
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 55M25
zbMATH DE Number: 7390135
zbMATH Keywords: Toeplitz matrix
zbMATH Keywords: Kac-Murdock-Szegő matrix
zbMATH Keywords: eigenvalues
zbMATH Keywords: contour lines
zbMATH Keywords: level curves
zbMATH Keywords: curve winding numbers
MaRDI profile type: Publication
OpenAlex ID: W3184293233
arXiv ID: 2104.11527
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DOI: 10.1016/J.LAA.2021.07.016
describes a project that uses: Digital Library of Mathematical Functions
description: scientific article