The <i>W</i> -weighted <i>m</i> -weak group MP inverse and its applications

We extend the concept of the m-weak group MP inverse of a square matrix to a rectangular matrix, called the W-weighted m-weak group MP inverse, which also unifies the W-weighted weak core inverse and W-weighted DMP inverse. Some properties, characterizations, and representations of this new generalized inverse are shown. Additionally, applications of the W-weighted m-weak group MP inverse are presented in solving a constrained optimization problem and a class of consistent matrix equations. Several numerical examples are proposed to illustrate some results given in the paper.