On the perturbation of the Moore–Penrose inverse of a matrix

摘要

The Moore–Penrose inverse of a matrix has been extensively investigated and widely applied in many fields over the past decades. One reason for the interest is that the Moore–Penrose inverse can succinctly express some important geometric constructions in finite-dimensional spaces, such as the orthogonal projection onto a subspace and the linear least squares problem. In this paper, we establish new perturbation bounds for the Moore–Penrose inverse under the Frobenius norm, some of which are sharper than the existing ones.