Weighted MP-m-weak group inverse

UDC 519. 6 In order to generalize the concepts of weighted MPWG inverse and MP-m-weak group inverse, we consider systems of matrix equations, which are extensions of systems used to define these concepts. To solve new extended systems, we introduce the notion of weighted MP-m-weak group inverse. Numerous characterizations and representations of the weighted MP-m-weak group inverse are proposed. Thus, we extend known results for the weighted MPWG inverse and MP-m-weak group inverse. We solve some systems of linear equations and express their solutions by applying the weighted MP-m-weak group inverse.