A note on the representation and approximation of the outer inverse AT,S(2) of a matrix A

摘要

In this note, we present a unified representation and an approximation theorem for the outer inverse AT,S(2) of a matrix A, which is the matrix X satisfying XAX=X, R(X)=T, N(X)=S. Based on the new approximation theorem, we can develop several expressions and computational procedures for the generalized inverse AT,S(2), which improve the recent work on this topic.