Research reveals conditions for the additivity of Moore-Penrose inverses in invertible matrices, indicating important mathematical relationships.
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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Milenković et al. (2025) studied this question.
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