In the last decades the Moore-Penrose pseudoinverse has found a wide range of applications

in many areas of Science and became a useful tool for different scientists dealing with

optimization problems, data analysis, solutions of linear integral equations, etc. At fi rst

we will present a review of some of the basic results on the so-called Moore-Penrose

pseudoinverse of matrices, a concept that generalizes the usual notion of inverse of a square

matrix, but that is also applicable to singular square matrices or even to non-square matrices