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

In this paper, we establish a basic representation and a representation theorem for the outer inverse AT,S(2) of a matrix A, which is the matrix X satisfyingimageXAX=X, R(X)=T and N(X)=S.We develop several specific representations and iterative methods for AT,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.