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Nonnegative Moore-Penrose Inverse of Gram Matrices in an Indefinite Inner Product Space

Author

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  • K. Ramanathan

    (Jerusalem College of Engineering)

  • K. C. Sivakumar

    (Indian Institute of Technology Madras)

Abstract

In this paper, we derive necessary and sufficient conditions for the nonnegativity of the Moore-Penrose inverse of a Gram matrix defined in an indefinite inner product space using indefinite matrix multiplication. These conditions include the acuteness of a pair of closed convex cones.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:140:y:2009:i:1:d:10.1007_s10957-008-9450-y
    DOI: 10.1007/s10957-008-9450-y
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    References listed on IDEAS

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    1. 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.
    2. K. C. Sivakumar, 2006. "Proof by Verification of the Greville/Udwadia/Kalaba Formula for the Moore-Penrose Inverse of a Matrix," Journal of Optimization Theory and Applications, Springer, vol. 131(2), pages 307-311, November.
    3. F. E. Udwadia & P. Phohomsiri, 2006. "Recursive Formulas for the Generalized LM-Inverse of a Matrix," Journal of Optimization Theory and Applications, Springer, vol. 131(1), pages 1-16, October.
    4. F. E. Udwadia & P. Phohomsiri, 2005. "Recursive Determination of the Generalized Moore–Penrose M-Inverse of a Matrix," Journal of Optimization Theory and Applications, Springer, vol. 127(3), pages 639-663, December.
    5. 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.
    6. F.E. Udwadia & R.E. Kalaba, 2003. "Sequential Determination of the {1, 4}-Inverse of a Matrix," Journal of Optimization Theory and Applications, Springer, vol. 117(1), pages 1-7, April.
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