Expressions and characterizations for the Moore-Penrose inverse of operators and matrices
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Abstract
Under certain conditions, we prove that the Moore-Penrose inverse of a sum of operators is the sum of the Moore-Penrose inverses. From this, we derive expressions and characterizations for the Moore-Penrose inverse of an operator that are useful for its computation. We give formulations of them for finite matrices and study the Moore-Penrose inverse of circulant matrices and of distance matrices of certain graphs.
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