Using rank factorization in calculating the Moore-Penrose generalized inverse
J. Parks-Gornet, Ibrahim N. Imam · 2003
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/sup T/B)/sup -1/ and (CC/sup T/)/sup -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.>