00000cmm a22000004a 4500 UP-99796217611212497 Buklod 20230215085534.0 m go j cr |n |||auu|a 110406s2011 xxu u eng d 1441998861(eBook) 9781441998866(eBook) (iLib)UPD-00215704275 DLC DML eng DMLUC QA 188 Y36 2011eb Yanai, Haruo 1940- Projection matrices, generalized inverse matrices, and singular value decomposition Haruo Yanai, Kei Takeuchi, Yoshio Takane. New York Springer 2011 1 online resources (xi, 234p.) Statistics for social and behavioral sciences 1. Fundamentals of linear algebra -- 2. Projection matrices -- 3. Generalized inverse matrices -- 4. Explicit representations -- 5. Singular value decomposition (SVD) -- 6. Various applications -- 7. Answers to Exercises -- 8. References. IP-based subscription, access limited to within on campus computer network. Access via Electronic Resources of the UPD University Library Website. 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. Electronic reproduction. New York SpringerLink 2011. Available via World Wide Web through SpringerLink. Matrices. Decomposition method. Matrix inversion. Algebras, Linear. Electronic books. Takeuchi, Kei 1933-. Takane, Yoshio. SpringerLink (Online service). Electronic Resource Available for University of the Philippines Diliman via SpringerLink. Click here to access http://link.springer.com/book/10.1007/978-1-4419-9887-3 FO Monograph UPD DMLR Electronic Resource