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.
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Udwadia, F.E., Kalaba, R.E. An Alternative Proof of the Greville Formula. Journal of Optimization Theory and Applications 94, 23–28 (1997). https://doi.org/10.1023/A:1022699317381
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DOI: https://doi.org/10.1023/A:1022699317381