Abstract
Generalized inverses of a matrix product can be written as certain matrix expressions that are composed by the given matrices and their generalized inverses, and a challenging task in this respect is to establish various reasonable reverse order laws for generalized inverses of matrix products. In this paper, we present two groups of known and new mixed reverse order laws for the Moore–Penrose inverses of products of two and three matrices through various conventional matrix operations. We also establish four groups of matrix set inclusions that are composed by \(\{1\}\)- and \(\{1,2\}\)-generalized inverses of A, B, C, and their products AB and ABC.
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The author is grateful to an anonymous referee for his/her helpful comments and suggestions on an earlier version of this paper.
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Communicated by Jinyun Yuan.
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Tian, Y. Two groups of mixed reverse order laws for generalized inverses of two and three matrix products. Comp. Appl. Math. 39, 181 (2020). https://doi.org/10.1007/s40314-020-01203-w
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DOI: https://doi.org/10.1007/s40314-020-01203-w