Mathematics Faculty Articles

Title

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

Document Type

Article

Publication Date

12-1-2006

Publication Title

Linear Algebra and its Applications

Keywords

Diagonalizable and singular matrix, Simple invariant subspaces, Separation function, Relative perturbation bound

ISSN

0024-3795

Volume

419

Issue/No.

2-3

First Page

765

Last Page

771

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.

Comments

Under an Elsevier user license

AMS classification

  • 15A60;
  • 65F35

DOI

10.1016/j.laa.2006.06.015