Accession Number:

ADA636847

Title:

Relative Perturbation Theory: (I) Eigenvalue Variations

Descriptive Note:

Technical rept.

Corporate Author:

CALIFORNIA UNIV BERKELEY DEPT OF MATHEMATICS

Personal Author(s):

Report Date:

1994-07-25

Pagination or Media Count:

68.0

Abstract:

In this paper, we consider how eigenvalues of a matrix A change when it is perturbed to perturbed matrix A unperturbed D1 ADsub 2 and how singular values of a nonsquare matrix B change when it is perturbed to approximation of B unperturbed D1BDsub 2, where D1 and D2 are assumed to be close to unitary matrices of suitable dimensions. We have been able to generalize many well-known perturbation theorems, including Hoffman-Wielandt theorem and Weyl-Lidskii theorem. As applications, we obtained bounds for perturbations of graded matrices in both singular value problems and nonnegative definite Hermitian eigenvalue problems.

Subject Categories:

  • Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE