Abstract
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 subjects, such as the singular value 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 subject.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.