In this paper, we extend notions of the weighted core-EP right and left inverses, the weighted DMP and MPD inverses, and the CMP inverse to matrices over the quaternion skew field that have some features in comparison to these inverses over the complex field. We give the direct methods of their computing, namely, their determinantal representations by using noncommutative column and row determinants previously introduced by the author. A numerical example to illustrate the main result is given.

中文翻译：

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加权四元数核心-EP、DMP、MPD 和 CMP 的逆及其行列式表示

在本文中，我们将加权核心 EP 左右逆、加权 DMP 和 MPD 逆以及 CMP 逆的概念扩展到四元数偏斜场上的矩阵，与复数场上的这些逆相比，这些矩阵具有一些特征。我们给出了它们的直接计算方法，即使用作者之前介绍的非交换列和行行列式表示它们的行列式表示。给出了一个数值例子来说明主要结果。