Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition

· ·
· Springer Science & Business Media
电子书
236
评分和评价未经验证  了解详情

关于此电子书

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.

作者简介

Haruo Yanai is an educational psychologist and epidemiologist specialized in educational assessment and statistics. While he was developing an aptitude test as part of his doctoral dissertation at the University of Tokyo, he began his pioneering work on unifying various methods of multivariate analysis using projectors. This work has culminated in his widely acclaimed book “The Foundations of Multivariate Analysis” (Wiley Eastern, 1982) with Takeuchi and Mukherjee. He has held a professorial position in the Research Division at the National Center for University Entrance Examinations and is currently a Professor of Statistics at St. Luke College of Nursing in Tokyo. He is a former President of the Behaviormetric Society and is currently President of the Japan Testing Society.

Kei Takeuchi is a mathematical statistician with a strong background in economics. He was a Professor of Statistics in the Faculty of Economics at the University of Tokyo, and after retirement in the Faculty of International Studies at Meiji Gakuin University (now emeritus at both universities). The main fields of his research include the theory of mathematical statistics, especially asymptotic theory of estimation, multivariate analysis, and so on. He has published many papers and books on these subjects in both Japanese and English. He has also published articles on the Japanese economy, impact of science and technology on economy, etc. He is a former President of the Japan Statistical Society and Chairman of the Statistical Commission of Japan.

Yoshio Takane earned his Ph.D in quantitative psychology from the University of North Carolina in 1977. Since then he has been a Professor of Psychology at McGill University, specializing in quantitative methodology. He has developed a number of techniques for data analysis such as nonlinear multivariate analysis (MVA), maximum likelihood multidimensional scaling, latent variable models, methods for contingency table analysis, constrained principal component analysis and other structured MVA, and matrix theory associated with these developments. He has published widely in such journals as Psychometrika and Linear Algebra and Its Applications. He is a former President of the Psychometric Society.

为此电子书评分

欢迎向我们提供反馈意见。

如何阅读

智能手机和平板电脑
只要安装 AndroidiPad/iPhone 版的 Google Play 图书应用,不仅应用内容会自动与您的账号同步,还能让您随时随地在线或离线阅览图书。
笔记本电脑和台式机
您可以使用计算机的网络浏览器聆听您在 Google Play 购买的有声读物。
电子阅读器和其他设备
如果要在 Kobo 电子阅读器等电子墨水屏设备上阅读,您需要下载一个文件,并将其传输到相应设备上。若要将文件传输到受支持的电子阅读器上,请按帮助中心内的详细说明操作。