Characterizations of the Generalized MPCEP Inverse of Rectangular Matrices

In this paper, we introduce a new generalized inverse, called the G-MPCEP inverse of a complex matrix. We investigate some characterizations, representations, and properties of this new inverse. Cramer’s rule for the solution of a singular equation Ax=B is also presented. Moreover, the determinantal representations for the G-MPCEP inverse are studied. Finally, the G-MPCEP inverse being used in solving appropriate systems of linear equations is established.