On 2MP-, MP2- and C2MP-inverses for rectangular matrices

Abstract

This paper introduces 2MP-inverses, MP2-inverses, and C2MP-inverses, for rectangular matrices following a different approach to that used in the recent literature. These new inverses generalize some classical inverses in the literature. Instead of considering a system of matrix equations as usually, in order to define 2MP-inverses and MP2-inverses, we consider a construction from oblique projectors represented by means of outer generalized inverses. We use an adequate equivalence relation, and then we pass to the quotient set in order to get the most simple canonical representative. An interesting advantage of our extension of CMP inverses from square to rectangular matrices is that we do not need any auxiliary weight matrix, but we are using the own matrix A for doing it. In addition, some properties and representations of 2MP-, MP2-, and C2MP-inverses are given.