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Moore-Penrose Inverse of a Gram Matrix and Its Nonnegativity

Author

Listed:
  • T. Kurmayya

    (Indian Institute of Technology Madras)

  • K. C. Sivakumar

    (Indian Institute of Technology Madras)

Abstract

Let M=[A a] be a matrix of order m×n, where A∈ℝ m×(n−1) and a∈ℝ m is an m×1 vector. In this article, we derive a formula for the Moore-Penrose inverse of M * M and obtain sufficient conditions for its nonnegativity. The results presented here generalize the ones known earlier.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:139:y:2008:i:1:d:10.1007_s10957-008-9426-y
    DOI: 10.1007/s10957-008-9426-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. 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.
    3. 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.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

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    Keywords

    Moore-Penrose inverse; Gram matrix;

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