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Moore-Penrose Inverse of a Gram Matrix and Its Nonnegativity

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Abstract

Let M=[A  a] be a matrix of order m×n, where A∈ℝm×(n−1) and a∈ℝm 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.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600 036, India

    T. Kurmayya & K. C. Sivakumar

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  1. T. Kurmayya
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  2. K. C. Sivakumar
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Correspondence to T. Kurmayya.

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The authors thank the anonymous referee for suggestions on an earlier version that have resulted in an improved presentation.

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Kurmayya, T., Sivakumar, K.C. Moore-Penrose Inverse of a Gram Matrix and Its Nonnegativity. J Optim Theory Appl 139, 201–207 (2008). https://doi.org/10.1007/s10957-008-9426-y

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