A new equivalent condition of the reverse order law for G-inverses of multiple matrix products
Bing Zheng, Zhiping Xiong · Electronic Journal of Linear Algebra · 2008
In 1999, Wei [M.Wei, Reverse order laws for generalized inverse of multiple matrix products, Linear Algebra Appl., 293 (1999), pp. 273-288] studied reverse order laws for generalized inverses of multiple matrix products and derived some necessary and sufficient conditions for An{1}An−1{1} . . .A1{1} ⊆ (A1A2 . . .An){1} by using P-SVD (Product Singular Value Decomposition). In this paper, using the maximal rank of the generalized Schur complement, a new simpler equivalent condition is obtained in terms of only the ranks of the known matrices for this inclusion.