<i>m</i> -MP-weak Drazin matrices

The concepts of MP-w-D and w-D-MP matrices are defined based on the Moore-Penrose inverse in combination with a minimal rank weak Drazin inverse and a minimal rank right weak Drazin inverse. Using the [Formula: see text]th powers of a minimal rank weak Drazin inverse and a minimal rank right weak Drazin inverse instead of a minimal rank weak Drazin inverse and a minimal rank right weak Drazin inverse, we generalize the notions of MP-w-D and w-D-MP matrices and present the [Formula: see text]-MP-w-D and [Formula: see text]-w-D-MP matrices as new classes of square matrices. Recently considered [Formula: see text], [Formula: see text], MP-w-D and w-D-MP matrices are special types of [Formula: see text]-MP-w-D and [Formula: see text]-w-D-MP matrices and we study wider classes of matrices. We verify many characterizations and representations of our new types of matrices. New particular kinds of [Formula: see text]-MP-w-D and [Formula: see text]-w-D-MP matrices are investigated too. Applying the [Formula: see text]-MP-w-D and [Formula: see text]-w-D-MP matrices, we solve several linear equations.