Relative Perturbation Theory: (II) Eigenspace Variations
CALIFORNIA UNIV BERKELEY DEPT OF MATHEMATICS
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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.
- Theoretical Mathematics