The generalized weighted Moore-Penrose inverse

Abstract

In this paper, we definite a generalized weighted Moore-Penrose inverse A M,N + of a given matrixA, and give the necessary and sufficient conditions for its existence. We also prove its uniqueness and give a representation of it. In the end we point out this generalized inverse is also a prescribed rangT and null spaceS of {2}-(or outer) inverse ofA.