The Generalized Inverse A(2)T, Sof a Matrix Over an Associative Ring
Yaoming Yu, Guorong Wang · Journal of the Australian Mathematical Society · 2007
Abstract In this paper we establish the definition of the generalized inverse A(2)T, Swhich is a {2} inverse of a matrixAwith prescribed imageTand kernelsover an associative ring, and give necessary and sufficient conditions for the existence of the generalized inverse and some explicit expressions for 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 matrixAover an associative ring, the Drazin inverse Ad, the group inverse Agand the Moore-Penrose inverse . if they exist, are all the generalized inverse A(2)T, S.