Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition.pdf

Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition PDF

Yoshio Takane

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 it is closely related to the former. The book provides systematic and in-depth accounts of these concepts from a unified viewpoint of linear transformations finite dimensional vector spaces. More specially, it shows that projection matrices (projectors) and g-inverse matrices can be defined in various ways so that a vector space is decomposed into a direct-sum of (disjoint) subspaces. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition will be useful for researchers, practitioners, and students in applied mathematics, statistics, engineering, behaviormetrics, and other fields.

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2.35 MB DATEIGRÖSSE
1461428599 ISBN
Englisch SPRACHE
Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition.pdf

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Sofia Voigt

Projection matrices, generalized inverse matrices, …

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Matteo Müller

We employ the generalized inverse matrix of Moore-Penrose to study the existence and ... Keywords: Linear systems, SVD, Least squares technique, Pseudoinverse of Moore- ... Thus, the Singular Value Decomposition (SVD) ... [16 ] H. Yanai, K. Takeuchi, Y. Takane, Projection matrices, generalized inverse matrices,.

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Noel Schulze

Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition (Statistics for Social and Behavioral Sciences) (English Edition) [Kindle edition] by Yanai, Haruo, Takeuchi, Kei, Takane, Yoshio. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Projection Matrices, Generalized Projection Matrices& Generalized Inverse …

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Jason Lehmann

springer, 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

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Jessica Kohmann

06.05.2016 · The SVD factors each matrix into an orthogonal matrix times a diagonal matrix (the singular value) times another orthogonal matrix: rotation times stretch times rotation. License: Creative Commons Singular value decomposition - Wikipedia