Relative Perturbation Theory: (II) Eigenspace Variations

Abstract

In this paper, we consider how eigenspaces of a Hermitian matrix A change when it is perturbed to ~ A = D * AD and how singular values of a (nonsquare) matrix B change when it is perturbed to ~ B = D1 BD2, where D, D1 and D2 are assumed to be close to identity matrices of suitable dimensions, or either D1 or D2 close to some unitary matrix. We have been able to generalize well-known Davis-Kahan sin theta theorems. As applications, we obtained bounds for perturbations of graded matrices.

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Document Details

Document Type
Technical Report
Publication Date
Jul 25, 1994
Accession Number
ADA636848

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  • Ren-cang Li

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  • University of California, Berkeley

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