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

Abstract

[EN] 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 (n × n)-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 corenilpotent decomposition, the CMP and the CR inverses of some infinite matrices.