Eigenvalues of rank-one updated matrices with some applications

被引：121

作者：

Ding, Jiu ^{[1
]}

Zhou, Aihui

机构：

[1] Univ So Mississippi, Dept Math, Hattiesburg, MS 39406 USA

[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2007年 / 20卷 / 12期

基金：

中国国家自然科学基金;

关键词：

rank-one update; determinant; spectrum;

D O I：

10.1016/j.aml.2006.11.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a spectral perturbation theorem for rank-one updated matrices of special structure. Two applications of the result are given to illustrate the usefulness of the theorem. One is for the spectrum of the Google matrix and the other is for the algebraic simplicity of the maximal eigenvalue of a positive matrix. (c) 2007 Elsevier Ltd. All rights reserved.

引用

页码：1223 / 1226

页数：4

共 9 条

[1] [Anonymous], 2003, 2 EIGENVALUE GOOGLE
[2] Bapat RB., 1997, NONNEGATIVE MATRICES
[3] The anatomy of a large-scale hypertextual Web search engine
Brin, S
Page, L
[J]. COMPUTER NETWORKS AND ISDN SYSTEMS, 1998, 30 (1-7): : 107 - 117
[4] ELDEN L, 2003, LITHMATR0401
[5] Adaptive methods for the computation of PageRank
Kamvar, S
Haveliwala, T
Golub, G
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 386 : 51 - 65
[6] Langville A., 2004, INTERNET MATH, V1, P335, DOI DOI 10.1080/15427951.2004.10129091
[7] A survey of eigenvector methods for Web information retrieval
Langville, AN
Meyer, CD
[J]. SIAM REVIEW, 2005, 47 (01) : 135 - 161
[8] Minc H., 1988, Nonnegative Matrices
[9] Motwani R., 1998, TECHNICAL REPORT

← 1 →