Representation and approximation of the outer inverse AT,S(2) of a matrix A

Abstract In this paper, we establish a basic representation and a representation theorem for the outer inverse A T,S (2) of a matrix A, which is the matrix X satisfying XAX=X, R(X)=T and N(X)=S. We develop several specific representations and iterative methods for A T,S (2) . We show that this representation includes many of the traditional generalized inverses and outer inverses, and the relation of our results to these outer inverses will be explored.

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