Using rank factorization in calculating the Moore-Penrose generalized inverse

The rank factorization method is used to calculate the Moore-Penrose inverse of any arbitrary real m×n matrix A. The rank factorization method uses the fact that any matrix A of rank r can be factored as A=BC, where B is an m×r matrix of rank r and C is an r× n matrix of rank r. Using this factorization and other facts from matrix theory, the problem is reduced to that of calculating (B^TB)^-1 and (CC^T )^-1. After deriving an algorithm for calculating the Moore-Penrose inverse, the authors wrote a software package to perform the necessary computations and the actual generation of the Moore-Penrose inverse