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In this paper, we extend notions of the weighted core-EP right and leftinverses, the weighted DMP and MPD inverses, and the CMP inverse to matricesover the quaternion skew field H that have some features in comparison to theseinverses over the complex field. We give the direct methods of their computing,namely, their determinantal representations by using noncommutative column androw determinants previously introduced by the author. As the special cases, byusing the usual determinant, we give their determinantal representations formatrices with complex entries as well. A numerical example to illustrate themain result is given.

Determinantal representations of the weighted core-EP, DMP, MPD, and CMP inverses of matrices with quaternion and complex elements