Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition

Aside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of on...

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Detalles Bibliográficos
Autores principales: Yanai, Haruo, Takeuchi, Kei, Takane, Yoshio
Lenguaje:eng
Publicado: Springer 2011
Materias:
Mathematical Physics and Mathematics
Acceso en línea:https://dx.doi.org/10.1007/978-1-4419-9887-3
http://cds.cern.ch/record/1414711
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author Yanai, Haruo
Takeuchi, Kei
Takane, Yoshio
author_facet Yanai, Haruo
Takeuchi, Kei
Takane, Yoshio
author_sort Yanai, Haruo
collection CERN
description Aside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because
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institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2011
publisher Springer
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spelling cern-14147112021-04-22T00:39:29Zdoi:10.1007/978-1-4419-9887-3http://cds.cern.ch/record/1414711engYanai, HaruoTakeuchi, KeiTakane, YoshioProjection Matrices, Generalized Inverse Matrices, and Singular Value DecompositionMathematical Physics and MathematicsAside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because Springeroai:cds.cern.ch:14147112011
spellingShingle Mathematical Physics and Mathematics
Yanai, Haruo
Takeuchi, Kei
Takane, Yoshio
Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition
title Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition
title_full Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition
title_fullStr Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition
title_full_unstemmed Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition
title_short Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition
title_sort projection matrices, generalized inverse matrices, and singular value decomposition
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-1-4419-9887-3
http://cds.cern.ch/record/1414711
work_keys_str_mv AT yanaiharuo projectionmatricesgeneralizedinversematricesandsingularvaluedecomposition
AT takeuchikei projectionmatricesgeneralizedinversematricesandsingularvaluedecomposition
AT takaneyoshio projectionmatricesgeneralizedinversematricesandsingularvaluedecomposition

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