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Relative Perturbation Theory: (II) Eigenspace Variations

Authors:
Li, Ren-Cang
Technical Report Identifier: CSD-94-856
December 1994
CSD-94-856.pdf
CSD-94-856.ps

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 = D1BD2, 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.