Representations and properties for the MPCEP inverse

Our contribution is the development of novel representations and investigations of main properties of the MPCEP inverse. Precisely, we present representations of the MPCEP inverse which involve appropriate Moore–Penrose inverses, projections and full-rank decompositions, as well as limit and integral representations. Determinantal representations for the MPCEP inverse are also established. We study perturbation formulae with perturbation bounds of MPCEP inverse. An equivalent condition for the continuity of the MPCEP inverse is proposed. The MPCEP inverse of a suitable upper block triangular matrix is given. The successive matrix squaring algorithm and splitting method for computing the MPCEP inverse are presented. Some appropriate constrained systems of linear equations are solved applying the MPCEP inverse.