Inequalities of Rayleigh quotients and bounds on the spectral radius of nonnegative symmetric matrices
type: Item
instance of: scholarly article
title: Inequalities of Rayleigh quotients and bounds on the spectral radius of nonnegative symmetric matrices
zbMATH Open document ID: 0886.15013
DOI: 10.1016/S0024-3795(96)00534-4
author: Don Coppersmith
author: Alan J. Hoffman
author: Uriel G. Rothblum
published in: Linear Algebra and its Applications
publication date: 1998-04-23T00:00:00Z
review text: Let \(A\) be a nonnegative symmetric matrix, \(u\) be a nonnegative vector. \(Q_A(u)= u^TAu/ u^Tu\) is called the Rayleigh quotient of \(u\) under \(A\). The following result is obtained: \(Q_A (\sqrt{u\circ Au})\leq Q_A(u)\), where \(\sqrt{\;}\) denotes coordinatewise square roots and \(\circ\) is the Hadamard product. \(Q_A(Au)\) may be smaller than \(Q_A(u)\).
reviewed by: Tong Wenting
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 1067951
zbMATH Keywords: inequalities
zbMATH Keywords: bounds
zbMATH Keywords: spectral radius
zbMATH Keywords: nonnegative symmetric matrix
zbMATH Keywords: Rayleigh quotient
zbMATH Keywords: Hadamard product
MaRDI profile type: Publication
cites work: Q3943082
cites work: Nested Bounds for the Spectral Radius
cites work: Q5557602
cites work: Lower bounds for the Perron root of a nonnegative matrix
cites work: Nested bounds for the spectral radius
cites work: On the singular graph and the Weyl characteristic of an M-matrix
cites work: Algebraic eigenspaces of nonnegative matrices
cites work: Expansions of Sums of Matrix Powers
cites work: Q5342712
cites work: A computational method for the dominant root of a nonnegative irreducible matrix
Wikidata QID: Q127628830
description: scientific article; zbMATH DE number 1067951