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An Alternative Proof of the Greville Formula

Author

Listed:
  • F. E. Udwadia

    (University of Southern California)

  • R. E. Kalaba

    (University of Southern California)

Abstract

A simple proof of the Greville formula for the recursive computation of the Moore–Penrose (MP) inverse of a matrix is presented. The proof utilizes no more than the elementary properties of the MP inverse.

Suggested Citation

  • F. E. Udwadia & R. E. Kalaba, 1997. "An Alternative Proof of the Greville Formula," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 23-28, July.
    • Handle: RePEc:spr:joptap:v:94:y:1997:i:1:d:10.1023_a:1022699317381
    DOI: 10.1023/A:1022699317381
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    Citations

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    Cited by:

    1. K. Ramanathan & K. C. Sivakumar, 2009. "Nonnegative Moore-Penrose Inverse of Gram Matrices in an Indefinite Inner Product Space," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 189-196, January.
    2. T. Kurmayya & K. C. Sivakumar, 2008. "Moore-Penrose Inverse of a Gram Matrix and Its Nonnegativity," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 201-207, October.
    3. F. E. Udwadia & R. E. Kalaba, 1999. "General Forms for the Recursive Determination of Generalized Inverses: Unified Approach," Journal of Optimization Theory and Applications, Springer, vol. 101(3), pages 509-521, June.
    4. K. C. Sivakumar & J. M. Swarna, 2009. "Linear Optimization with Box Constraints in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 377-387, May.

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