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 -