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Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition / by Haruo Yanai, Kei Takeuchi, Yoshio Takane
(Statistics for Social and Behavioral Sciences. ISSN:21997365)
版 | 1st ed. 2011. |
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出版者 | (New York, NY : Springer New York : Imprint: Springer) |
出版年 | 2011 |
本文言語 | 英語 |
大きさ | XII, 236 p : online resource |
著者標目 | *Yanai, Haruo author Takeuchi, Kei author Takane, Yoshio author SpringerLink (Online service) |
件 名 | LCSH:Statistics LCSH:Biometry FREE:Statistics FREE:Biostatistics |
一般注記 | Fundamentals of Linear Algebra -- Projection Matrices -- Generalized Inverse Matrices -- Explicit Representations -- Singular Value Decomposition (SVD) -- Various Applications 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 HTTP:URL=https://doi.org/10.1007/978-1-4419-9887-3 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9781441998873 |
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電子リソース |
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EB00229650 |
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