Geodesic
A new equivalent condition of the reverse order law for $G$-inverses of multiple matrix products
The electronic journal of linear algebra, Tome 17 (2008), pp. 1-8.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 A n 1A n - 1 1 $\cdot \cdot \cdot A 1$ 1 $\subseteq $(A 1 A $2 \cdot \cdot \cdot A$ n ) 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.
Classification : 15A03, 15A09
Keywords: reverse order law, generalized inverse, matrix product, maximal rank, generalized Schur complement 
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Zheng, Bing; Xiong, Zhiping. A new equivalent condition of the reverse order law for $G$-inverses of multiple matrix products. The electronic journal of linear algebra, Tome 17 (2008), pp. 1-8. http://geodesic.mathdoc.fr/item/ELA_2008__17__a44/