Core-Nilpotent decomposition and new generalized inverses of finite potent endomorphisms

Abstract

ABSTRACT The aim of this work is to prove the existence and uniqueness of a core-nilpotent decomposition of finite potent endomorphisms on arbitrary vector spaces. This decomposition generalized the well-known core-nilpotent decomposition of complex -matrices. As an application we offer the definition and properties of the CMP inverse and of a new CR inverse for these linear maps. In particular, from the results of this work it is possible to compute the core-nilpotent decomposition, the CMP and the CR inverses of some infinite matrices.