Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition Hardcover - 2011 - 2011th Edition
by Haruo Yanai; Kei Takeuchi; Yoshio Takane
From the rear cover
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.
Details
- Title Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition
- Author Haruo Yanai; Kei Takeuchi; Yoshio Takane
- Binding Hardcover
- Edition number 2011th
- Edition 2011
- Pages 236
- Volumes 1
- Language ENG
- Publisher Springer
- Date 2011-04-12
- Illustrated Yes
- Features Bibliography, Illustrated, Index, Table of Contents
- ISBN 9781441998866 / 1441998861
- Weight 1.19 lbs (0.54 kg)
- Dimensions 6.62 x 9.48 x 0.82 in (16.81 x 24.08 x 2.08 cm)
- Library of Congress subjects Matrices, Algebras, Linear
- Library of Congress Catalog Number 2011925655
- Dewey Decimal Code 519.5
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Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition
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Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition (Statistics for Social and Behavioral Sciences)
by Yanai, Haruo; Takeuchi, Kei; Takane, Yoshio
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