Relative Perturbation Bounds for the Eigenvalues of Diagonalizable and Singular Matrices – Application of Perturbation Theory for Simple Invariant Subspaces

Authors

Yimin Wei, Fudan UniversityFollow
Xiezhang Li, Georgia Southern UniversityFollow
Fanbin Bu, Fudan UniversityFollow
Fuzhen Zhang, Nova Southeastern University- Fort LauderdaleFollow

Document Type

Article

Publication Date

12-1-2006

Publication Title

Linear Algebra and Its Applications

DOI

10.1016/j.laa.2006.06.015

ISSN

0024-3795

Abstract

Perturbation bounds for the relative error in the eigenvalues of diagonalizable and singular matrices are derived by using perturbation theory for simple invariant subspaces of a matrix and the group inverse of a matrix. These upper bounds are supplements to the related perturbation bounds for the eigenvalues of diagonalizable and nonsingular matrices.

Recommended Citation

Wei, Yimin, Xiezhang Li, Fanbin Bu, Fuzhen Zhang. 2006. "Relative Perturbation Bounds for the Eigenvalues of Diagonalizable and Singular Matrices – Application of Perturbation Theory for Simple Invariant Subspaces." Linear Algebra and Its Applications, 419 (2-3): 765-771. doi: 10.1016/j.laa.2006.06.015
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/575