A new relative perturbation theorem for singular subspaces

This note addresses the sensitivity of singular subspaces of a matrix under relative perturbations. It employs a new technique of separating a multipl icative perturbation D into two components: one is the distance of st scala r multiple of D to the nearest unitary matrix Q and the other is the distan ce 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. (C) 2000 Elsevier Science Inc. All rights re served.