On the ``Reverse Order Law'' Related to the Generalized Inverse of Matrix Products

The “reverse order law” related to ordinary inverses of matrix products, i.e., (<italic>AB</italic>)<supscrpt>-1</supscrpt> = <italic>B</italic><supscrpt>-1</supscrpt><italic>A</italic><supscrpt>-1</supscrpt>, is generally not transferable to the generalized inverse. There are, however, applications in which the reverse order law related to the generalized inverse reveals interesting properties in certain classes of matrices. In this paper, some necessary and sufficient conditions for the reverse order property to hold are given.

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