New Characterizations of the generalized B-T inverse

Abstract

Characterizations and explicit expressions of the generalized B-T inverse are given, this generalized inverse exists for any square matrix and any integer.
The relationships between the generalized B-T inverse and some well-known generalized inverses are investigated. Moreover, an explicit formula of the generalized B-T inverse is given by using Hartwig-Spindelb\"{o}ck decomposition.