The forward order law for generalized inverses has potential applications in numerical linear algebra, control theory, and statistics. This topic has attracted considerable attention. In this article, we present a necessary and sufficient condition for the forward order law (A1A2⋯An)Mn+1,M1†=(A1)M2,M1†(A2)M3,M2†⋯(An)Mn+1,Mn† by using the rank equalities of some generalized Schur complements. The topic is relevant and timely, and the results generalize existing work on unweighted and two-product cases.
No takes yet. Share an insight, caveat, or question.
Pan et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: