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 also explored. Through one-sided core and dual-core inverses, we have shown the existence of a generalized weighted Moore-Penrose inverse of matrices. Further, by applying a new representation and using the properties of the weighted core inverse of a matrix, we discuss some new results related to the reverse order law for these inverses.

翻译：本文引入了矩阵加权核心逆的新表示与刻画方法，探讨了这些逆的若干性质及其与其他广义逆之间的关联。通过单侧核心逆与对偶核心逆，我们证明了矩阵的广义加权Moore-Penrose逆的存在性。进一步地，利用矩阵加权核心逆的新表示及其性质，讨论了与这些逆的反序律相关的一些新结果。