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.

矩阵乘积的广义逆可以写成由给定矩阵及其广义逆组成的某些矩阵表达式，这方面的一项艰巨任务是为矩阵乘积的广义逆建立各种合理的逆序定律。在本文中，我们介绍了两组已知的和新的混合逆序定律，它们是通过各种常规矩阵运算得出的两个和三个矩阵的乘积的Moore-Penrose逆。我们还建立了四组矩阵集包含，它们由A，B，C及其乘积AB和A的\（\ {1 \} \） -和\（\ {1,2 \} \）-广义逆组成。美国广播公司。