A new relative perturbation theorem for singular subspaces (Q1579512)

This paper concerns the sensitivity of singular subspaces of a rectangular matrix under relative perturbations. Bounds are obtained by separating a multiplicative perturbation \(D\) into two components, one being the distance from a scalar multiple of \(D\) to the nearest unitary matrix \(Q\) and the other the distance from \(Q\) to the identity. Hence these bounds show how left and right multiplicative perturbations affect left and right singular subspaces.