In this paper, we introduce new representation and characterization of the
weighted core inverse of matrices. Several properties of these inverses and
their interconnections with other generalized inverses are explored. Through
one-sided core and dual-core inverse, the existence of a generalized weighted
Moore-Penrose inverse of matrices is proposed. Further, by applying a new
representation and using the properties of the weighted core inverse of a
matrix, we discuss a few new results related to the reverse order law for these
inverses.Comment: 18 page