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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....

Title : Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition (Statistics for Social and Behavioral Sciences)
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ISBN : 1441998861
Format Type : Hardcover
Language : English
Publisher : Springer 2011 edition April 12, 2011
Number of Pages : 236 pages
File Size : 995 KB
Status : Available For Download
Last checked : 21 Minutes ago!

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