A characterization and determinantal formula for the generalized inverse \(A^{(2)}_{T,S}\) and its applications.
This paper deals with the generalized inverse \(A^{(2)}_{S,T}\). A determinantal formula extending to the Cramer rule for this generalized inverse is obtained. This result can be used to derive the corresponding determinantal formula for the Moore-Penrose inverse, the weigthed Moore-Penrose inverse, the Drazin inverse, and so on. In addition, this result is applied to solve restricted linear systems.
scientific article; zbMATH DE number 1860994