Eigenvalues of rank-one updated matrices with some applications

doi:10.1016/j.aml.2006.11.016

Applied Mathematics Letters

Volume 20, Issue 12, December 2007, Pages 1223-1226

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Abstract

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.

Keywords

Rank-one update

Determinant

Spectrum

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^☆: This work was supported by the National Natural Science Foundation of China (Grant No. 10425105) and subsidized by the Special Funds for Major State Basic Research Projects (Grant No. 2005CB321704).

Applied Mathematics Letters

Eigenvalues of rank-one updated matrices with some applications☆

Abstract

Keywords