TY - JOUR T1 - A new relative perturbation theorem for singular subspaces JF - Linear Algebra and its Applications Y1 - 2000 A1 - Li,Ren-Cang A1 - Stewart, G.W. KW - Multiplicative perturbation KW - Relative gap KW - Relative perturbation theory KW - Singular subspace AB - 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. VL - 313 SN - 0024-3795 UR - http://www.sciencedirect.com/science/article/pii/S0024379500000744 CP - 1–3 M3 - 10.1016/S0024-3795(00)00074-4 ER -