Some results on symmetric circulant matrices and on symmetric centrosymmetric matrices
type: Item
instance of: scholarly article
title: Some results on symmetric circulant matrices and on symmetric centrosymmetric matrices
zbMATH Open document ID: 1063.15006
author: Oscar Rojo
author: Héctor Rojo
published in: Linear Algebra and its Applications
publication date: 2004-11-26T00:00:00Z
full work available at URL: http://hdl.handle.net/10533/175016
review text: The authors derive a useful sufficient condition for the existence of a non-negative symmetric circulant matrix having a prescribed spectrum. They, moreover, prove that any set \(\lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_n\) of real numbers is the spectrum of real symmetric centrosymmetric matrices \(S_1\) and \(S_2\) such that an eigenvector of \(S_1\) for the eigenvalue \(\lambda_1\) is the all-ones vector and an eigenvector of \(S_2\) for the eigenvalue \(\lambda_1\) is the vector consisting of the entry \((-1)^{i-1}\) in the \(i\)-th component. The authors also propose an algorithm to compute the eigenvalues of some real symmetric centrosymmetric matrices, based on fast Fourier transform.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A29
zbMATH DE Number: 2119136
zbMATH Keywords: centrosymmetric matrices
zbMATH Keywords: Toeplitz matrices
zbMATH Keywords: Hankel matrices
zbMATH Keywords: circulant matrix
zbMATH Keywords: prescribed spectrum
zbMATH Keywords: algorithm
zbMATH Keywords: eigenvalues
zbMATH Keywords: inverse eigenvalue problem
zbMATH Keywords: fast Fourier transform
MaRDI profile type: Publication
OpenAlex ID: W1981073055
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DOI: 10.1016/J.LAA.2004.06.013
description: scientific article; zbMATH DE number 2119136