The Moore-Penrose Pseudoinverse: A Tutorial Review of the Theory
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| Format: | Artículo científico |
| Sprache: | en |
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Sociedade Brasileira de Física
2012
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| _version_ | 1876476134965641216 |
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| author | João Carlos Alves Barata |
| author_facet | João Carlos Alves Barata |
| contents | The Moore-Penrose Pseudoinverse: A Tutorial Review of the Theory João Carlos Alves Barata Mahir Saleh Hussein Física, Astronomía y Matemáticas Moore Penrose pseudoinverse Singular values decomposition 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. 2012 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46423428019 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.1-2 Vol.42 |
| format | Artículo científico |
| id | redalyc_46423428019 |
| institution | Redalyc |
| language | en |
| publishDate | 2012 |
| publisher | Sociedade Brasileira de Física |
| spellingShingle | The Moore-Penrose Pseudoinverse: A Tutorial Review of the Theory João Carlos Alves Barata Física, Astronomía y Matemáticas Moore Penrose pseudoinverse Singular values decomposition The Moore-Penrose Pseudoinverse: A Tutorial Review of the Theory João Carlos Alves Barata Mahir Saleh Hussein Física, Astronomía y Matemáticas Moore Penrose pseudoinverse Singular values decomposition 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. 2012 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46423428019 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.1-2 Vol.42 |
| title | The Moore-Penrose Pseudoinverse: A Tutorial Review of the Theory |
| topic | Física, Astronomía y Matemáticas Moore Penrose pseudoinverse Singular values decomposition |
| url | https://www.redalyc.org/articulo.oa?id=46423428019 |