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.
Title
Relative Perturbation Theory: (II) Eigenspace Variations
Published
1994-12-01
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
CSD-94-856
Type
Text
Extent
35 p
Archive
The Engineering Library
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