  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 H 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. As the special cases, by
using the usual determinant, we give their determinantal representations for
matrices with complex entries as well. A numerical example to illustrate the
main result is given.
