ABSTRACT
This chapter presents the definitions, basic properties, and some methods for computing generalized inverses of constant matrices. It discusses some known methods for computing various generalized inverses of matrices. The chapter presents the several representations of generalized inverses, expressed in terms of full-rank factorizations and adequately selected matrices. It introduces the well-known Leverrier-Faddeev method and this algorithm has been rediscovered and modified several times. Although the algorithm is intriguingly beautiful, it is not practical for floating-point computations. The chapter shows extensions of Leverrier-Faddeev method which computes Moore-Penrose (MP) and Drazin inverse of an input matrix, respectively. The chapter deals with another class of well-known methods for computing generalized inverses and all these methods are finite iterative methods. Similarly to the Greville's method, it can be constructed the method for computing the weighted MP inverse of partitioned matrices.
