The Moore–Penrose Pseudoinverse: A Tutorial Review of the Theory
| Autor: | Mahir S. Hussein, João C. A. Barata |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Optimization problem
Computer science MATRIZES MathematicsofComputing_NUMERICALANALYSIS FOS: Physical sciences General Physics and Astronomy Mathematical Physics (math-ph) Spectral theorem Expression (computer science) Singular value Range (mathematics) Matrix (mathematics) Simple (abstract algebra) Calculus Mathematical Physics Moore–Penrose pseudoinverse |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| ISSN: | 1678-4448 0103-9733 |
| DOI: | 10.1007/s13538-011-0052-z |
| Popis: | 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. 23 pages |
| Databáze: | OpenAIRE |
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