Characterizations of the Weighted Core-EP Inverses

Following the popularity of the core-EP (c-EP) and weighted core-EP (w-c-EP) inverses, so called one-sided versions of the w-c-EP inverse are introduced recently in Behera et al. (Results Math 75:174 (2020). These extensions are termed as E-w-c-EP and F-w-d-c-EP g-inverses as well as the star E-w-c-EP and the F-w-d-c-EP star classes of g-inverses. The applicability of these g-inverses in solving certain restricted matrix equations has been verified. Several additional results on these classes of g-inverses are established in this paper. In addition, the Moore–Penrose E-w-c-EP inverse and the F-w-d-c-EP Moore–Penrose inverse are proposed using proper expressions that involve the Moore–Penrose inverse and the E-w-c-EP or F-we-d-c-EP inverse. Further, the W-weighted Moore–Penrose c-EP and the W-weighted c-EP Moore–Penrose g-inverses are considered with the aim to extend the considered w-c-EP generalized inverses to rectangular matrices. Characterizations, properties, representations and applications of these inverses are considered.