Moore-Penrose Inverse of some Linear Maps on Infinite-Dimensional Vector Spaces

Abstract

The aim of this work is to characterize linear maps of inner pro\-duct infinite-dimensional vector spaces where the Moore-Penrose inverse exists. This MP inverse generalizes the well-known Moore-Penrose inverse of a matrix $A\in {\text{Mat}}_{n\times m}(\mathbb{C})$. Moreover, a method for the computation of the MP inverse of some endomorphisms on infinite-dimensional vector spaces is given. As an application, we study the least norm solution of an infinite linear system from the Moore-Penrose inverse offered.

arXiv comment17 pages