On the characterization of the set of reflexive generalized inverses of finite potent endomorphisms

Abstract

[EN]The aim of this work is to characterize the set of reflexive generalized inverses of a finite potent endomorphism. As an application we determine the structure of the set of reflexive generalized inverses of an square matrix with entries in an arbitrary field and we offer an algorithm for the explicit computation of these matrices. Several examples of the given characterization are also provided.