  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 physicists
dealing, for instance, with optimization problems, with data analysis, with the
solution of linear integral equations, etc. The existence of such applications
alone should attract the interest of students and researchers in the
Moore-Penrose pseudoinverse and in related sub jects, like the singular values
decomposition theorem for matrices. In this note we present a tutorial review
of the theory of the Moore-Penrose pseudoinverse. We present the first
definitions and some motivations and, after obtaining some basic results, we
center our discussion on the Spectral Theorem and present an algorithmically
simple expression for the computation of the Moore-Penrose pseudoinverse of a
given matrix. We do not claim originality of the results. We rather intend to
present a complete and self-contained tutorial review, useful for those more
devoted to applications, for those more theoretically oriented and for those
who already have some working knowledge of the sub ject.
