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 Instead of considering system matrix equations as usually, order define 2MP-inverses we consider construction from oblique projectors represented by means outer generalized inverses. We use an adequate equivalence relation, then pass quotient set get most simple canonical representative. An interesting advantage our extension CMP square is do not need any auxiliary weight matrix, but are using own A doing it. In addition, properties representations 2MP-, MP2-, C2MP-inverses given.