1423	 A Simple Algorithm for Computing the Generalized Inverse of a Matrix	 The generalized inverse of a matrix is important in analysis because it provides an extension of the concept of an inverse which applies to all matrices. It also has many applications in numerical analysis but it is not widely used because the existing algorithms are fairly complicated and require considerable storage space. A simple extension has been found to the conventional orthogonalization method for inverting non-singular matrices which gives the generalized inverse with little extra effort and with no additional storage requirements. The algorithm gives the generalized inverse for any m by n matrix A including the special case when m n and A is non-singular and the case when m n and rank A n. In the first case the algorithm gives the ordinary inverse of A. In the second case the algorithm yields the ordinary least squares transformation matrix INV A A A and has the advantage of avoiding the loss of significance which results in forming the product A A explicitly.
