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

Abstract

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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Document Details

Document Type
Technical Report
Publication Date
Jun 22, 1984
Accession Number
ADA151736

Entities

People

  • G. P. Mccormick
  • S. G. Leaver

Organizations

  • George Washington University

Tags

Communities of Interest

  • Advanced Electronics
  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Computations
  • Curvature
  • Eigenvalues
  • Eigenvectors
  • Engineering
  • Iterations
  • Materials
  • Military Research
  • New York
  • Perturbations
  • Schools
  • Symmetry
  • Universities
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Game Theory.
  • Graph Algorithms and Convex Optimization.