Refined Perturbation Bounds for Eigenvalues of Hermitian and Non-Hermitian Matrices | Zendy

Ilse C. F. Ipsen | Zendy; Boaz Nadler | Zendy

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Refined Perturbation Bounds for Eigenvalues of Hermitian and Non-Hermitian Matrices

Author(s) -

Ilse C. F. Ipsen,

Boaz Nadler

Publication year - 2009

Publication title -

siam journal on matrix analysis and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.268

H-Index - 101

eISSN - 1095-7162

pISSN - 0895-4798

DOI - 10.1137/070682745

Subject(s) - hermitian matrix , eigenvalues and eigenvectors , mathematics , eigenvalue perturbation , eigendecomposition of a matrix , perturbation (astronomy) , hermitian symmetric space , mathematical analysis , rank (graph theory) , matrix norm , pure mathematics , hermitian manifold , combinatorics , physics , geometry , curvature , quantum mechanics , ricci curvature

We present eigenvalue bounds for perturbations of Hermitian matrices and express the change in eigenvalues in terms of a projection of the perturbation onto a particular eigenspace, rather than in terms of the full perturbation. The perturbations we consider are Hermitian of rank one, and Hermitian or non-Hermitian with norm smaller than the spectral gap of a specific eigenvalue. Applications include principal component analysis under a spiked covariance model, and pseudo-arclength continuation methods for the solution of nonlinear systems.

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