In this paper, we introduce the notation of $E$-weighted core-EP and $F$-weighted dual core-EP inverse of matrices. We then obtain a few explicit expressions for the weighted core-EP inverse of matrices through other generalized inverses. Further, we discuss the existence of generalized weighted Moore-Penrose inverse and additive properties of the weighted core-EP inverse of matrices. In addition to these, we propose the star weighted core-EP and weighted core-EP star class of matrices for solving the system of matrix equations. We further elaborate on this theory by producing a few representation and characterization of star weighted core-EP and weighted core-EP star classes of matrices.

中文翻译：

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矩阵加权 Core-EP 逆的进一步结果

在本文中，我们介绍了矩阵的 $E$-weighted core-EP 和 $F$-weighted dual core-EP 逆矩阵的符号。然后，我们通过其他广义逆获得矩阵的加权核心-EP 逆的一些显式表达式。此外，我们讨论了矩阵的加权核-EP 逆矩阵的广义加权摩尔-彭罗斯逆和可加性质的存在。除此之外，我们还提出了用于求解矩阵方程组的星形加权核心 EP 和加权核心 EP 星形类矩阵。我们通过生成一些星加权核心-EP 和加权核心-EP 星类矩阵的表示和表征来进一步阐述这个理论。