Some results on additivity of Moore-Penrose inverse in matrix settings

Jovana Milenković, Jovana Nikolov Radenković

Abstract


We present the necessary and sufficient conditions for the Moore-Penrose inverse of the sum of two
matrices to be equal to the sum of Moore-Penrose inverses of those matrices when these matrices are
invertible, or one matrix is invertible and the other satisfies certain range inclusions. Similar results are
presented for the group inverse.


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