Resumen de The generalized inverse A(2)TS of a matrix over an associative ring
In this paper we establish the definition of the generalized inverse A(2)TS which is a 2 inverse of a matrix A with prescribed image T and kernel S over an associative ring, and give necessary and sufficient conditions for the existence of the generalized inverse ATS(12) and some explicit expressions for ATS(12) of a matrix A over an associative ring, which reduce to the group inverse or 1 inverses. In addition, we show that for an arbitrary matrix A over an associative ring, the Drazin inverse Ad , the group inverse Ag and the Moore�Penrose inverse A , if they exist, are all the generalized inverse A(2)TS.
