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On mixed‐type reverse‐order laws for the Moore‐Penrose inverse of a matrix product

On mixed‐type reverse‐order laws for the Moore‐Penrose inverse of a matrix product

Some mixed‐type reverse‐order laws for the Moore‐Penrose inverse of a matrix product are established. Necessary and sufficient conditions for these laws to hold are found by the matrix rank method. Some applications and extensions of these reverse‐order laws to the weighted Moore‐Penrose inverse are also given.