Formulas for Updating the Generalized Inverse of a Symmetric Matrix Perturbed by a Symmeric Rank Two Matrix Composed of Two Nonsymmetric DYADS

摘要

In many applications employing a symmetric matrix and its generalized (Penrose-Moore) inverse the matrix is given in a natural way as the finite sum of symmetric dyadic matrices and pairs of nonsymmetric dyadic matrices. In this paper, formulas are given for the generalized inverse, B+, of B = A + abT + baT for A symmetric, a,b vectors. There are nine distinct cases which must be considered. The application of these formulas is given to the computation of an estimate of the positive part and directions of negative curvature for a symmetric matrix. (Author).