A weak group inverse for rectangular matrices (Q2331733)

In [\textit{D. E. Ferreyra} et al., Quaest. Math. 41, No. 2, 265--281 (2018; Zbl 1390.15010)], the authors defined the weighted core EP inverse. In this paper, the authors study the weak group inverse and the weighted core EP inverse of a matrix. They are computed by means of the core EP decomposition and the weighted core EP decomposition, respectively. The authors also compute the weighted Drazin inverse and the weighted group inverse using new methods. A new generalized inverse is presented as the unique solution of a system of matrix equations. Some properties, representations, and characterizations for weighted weak group inverses are investigated, and some relationships to well-known inverses are obtained.