An Elimination Method for Computing the Generalized Inverse of an Arbitrary Complex Matrix

where R ( A ) is the range of A in E "~ and PR(~) is the orthogonal projection on R ( A ) . A + is called the generalized inverse (g.i.) of A. I f A is nonsingular then A + = A-I ; otherwise A + still possesses properties 1 which make it a central concept in matr ix theory 2 and in numerical analysis. ~ Methods for computing the g.i. have been given by various authors: [12, 15, 8, 9, 4, 1]. In this paper we present an elimination method for computing A +. A G A T E 20 program for this method is given in [2].