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Formulas for Updating the Generalized Inverse of a Symmetric Matrix Perturbed by a Symmeric Rank Two Matrix Composed of Two Nonsymmetric DYADS,
GEORGE WASHINGTON UNIV WASHINGTON DC INST FOR MANAGEMENT SCIENCE AND ENGINEERING
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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.
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