1WG inverse of square matrices

Abstract

In this paper, we introduce a new generalized inverse, which is called 1WG inverse of complex square matrices. We investigate the existence and uniqueness for the 1WG inverse and give some characterizations, representations, and properties of it. Next, by using the core-EP decomposition, we discuss the relationships between the 1WG inverse and other generalized inverses. Successive matrix squaring algorithm is considered for calculating the 1WG inverse. In the end, we present a binary relation for the 1WG inverse.