A new relative perturbation theorem for singular subspaces

TitleA new relative perturbation theorem for singular subspaces
Publication TypeJournal Articles
Year of Publication2000
AuthorsLi R-C, Stewart G.W
JournalLinear Algebra and its Applications
Pagination41 - 51
Date Published2000/07/01/
ISBN Number0024-3795
KeywordsMultiplicative perturbation, Relative gap, Relative perturbation theory, Singular subspace

This note addresses the sensitivity of singular subspaces of a matrix under relative perturbations. It employs a new technique of separating a multiplicative perturbation D into two components: one is the distance of a scalar multiple of D to the nearest unitary matrix Q and the other is the distance of Q to the identity. Consequently, the new bounds reflect the intrinsic differences in how left and right multiplicative perturbations affect left and right singular subspaces.