Relative Perturbation Theory: (I) Eigenvalue Variations

Abstract

In this paper, we consider how eigenvalues of a matrix A change when it is perturbed to perturbed matrix A = unperturbed D(*/1) AD(sub 2) and how singular values of a (nonsquare) matrix B change when it is perturbed to approximation of B = unperturbed D(*/1)BD(sub 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.

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Document Details

Document Type
Technical Report
Publication Date
Jul 25, 1994
Accession Number
ADA636847

Entities

People

  • Ren-cang Li

Organizations

  • University of California, Berkeley

Tags

DTIC Thesaurus Topics

  • Complex Numbers
  • Computer Science
  • Decomposition
  • Eigenvalues
  • Equations
  • Identities
  • Inequalities
  • Mathematical Analysis
  • Mathematics
  • Numbers
  • Permutations
  • Perturbation Theory
  • Perturbations
  • Real Numbers
  • Sequences
  • Theorems
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra