Abstract
In this short note, we present a simple linear-algebraic proof, by verification, of the well-known Greville/Udwadia/Kalaba formula for computing the Moore-Penrose inverse of a matrix.
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Udwadia, F., and Kalaba, R. E., An Alternative Proof of the Greville Formula, Journal of Optimization Theory and Applications, Vol. 94, pp. 23–28, 1997.
Greville, T. N. E., Some Applications of the Pseudoinverse of a Matrix, SIAM Review, Vol. 2, pp. 15–22, 1960.
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Communicated by F.E. Udwadia
The author thanks the referee for a meticulous reading of the manuscript and for providing suggestions leading to a much simpler proof than the original proof. Indeed, the original proof used the avoidable notion of projection matrices.
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Sivakumar, K.C. Proof by Verification of the Greville/Udwadia/Kalaba Formula for the Moore-Penrose Inverse of a Matrix. J Optim Theory Appl 131, 307–311 (2006). https://doi.org/10.1007/s10957-006-9148-y
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DOI: https://doi.org/10.1007/s10957-006-9148-y