Cauchy's interlace theorem and lower bounds for the spectral radius
type: Item
instance of: scholarly article
title: Cauchy's interlace theorem and lower bounds for the spectral radius
zbMATH Open document ID: 0955.15007
DOI: 10.1155/S016117120000257X
author: Peter R. Mercer
author: A. McD. Mercer
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2000-08-27T00:00:00Z
full work available at URL: https://eudml.org/doc/48637
review text: A new proof is presented for the Cauchy interlace theorem (the theorem states that if a row-column pair is deleted from a real symmetric matrix \(A\), then the eigenvalues of the resulting matrix interlace those of the original ones). The proof comprises the case in which the matrix has distinct eigenvalues and the case of multiple eigenvalues. The lower bounds for the spectral radius of a real symmetric matrix are improved.
Mathematics Subject Classification ID: 15A42
zbMATH DE Number: 1496722
zbMATH Keywords: Cauchy interlace theorem
zbMATH Keywords: symmetric matrix
zbMATH Keywords: eigenvalues
zbMATH Keywords: lower bounds for the spectral radius
MaRDI profile type: Publication
OpenAlex ID: W2114617845
description: scientific article; zbMATH DE number 1496722