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Titlebook: Linear Algebra and Linear Models; R.B. Bapat Textbook 2012Latest edition Springer-Verlag London Limited 2012 linear algebra.linear model.m

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书目名称Linear Algebra and Linear Models
编辑R.B. Bapat
视频video
概述Provides a concise and rigorous introduction to linear algebra from the matrix theory viewpoint which is well-suited for statistical applications.Offers a compact introduction to estimation and testin
丛书名称Universitext
图书封面Titlebook: Linear Algebra and Linear Models;  R.B. Bapat Textbook 2012Latest edition Springer-Verlag London Limited 2012 linear algebra.linear model.m
描述.Linear Algebra and Linear Models comprises a concise and rigorous introduction to linear algebra required for statistics followed by the basic aspects of the theory of linear estimation and hypothesis testing. The emphasis is on the approach using generalized inverses. Topics such as the multivariate normal distribution and distribution of quadratic forms are included..For this third edition, the material has been reorganised to develop the linear algebra in the first six chapters, to serve as a first course on linear algebra that is especially suitable for students of statistics or for those looking for a matrix theoretic approach to the subject. Other key features include:. coverage of topics such as rank additivity, inequalities for eigenvalues and singular values;. a new chapter on linear mixed models;. over seventy additional problems on rank: the matrix rank is an important and rich topic with connections to many aspects of linear algebra such as generalized inverses, idempotent matrices and partitioned matrices..This text is aimed primarily at advanced undergraduate and first-year graduate students taking courses in linear algebra, linear models, multivariate analysis and d
出版日期Textbook 2012Latest edition
关键词linear algebra; linear model; mixed effects model; normal equations; variance components; variance-covari
版次3
doihttps://doi.org/10.1007/978-1-4471-2739-0
isbn_softcover978-1-4471-2738-3
isbn_ebook978-1-4471-2739-0Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer-Verlag London Limited 2012
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Generalized Inverses,y if it has the same rank as the matrix. Least squares and minimum norm inverses are defined and their characterization in terms of linear equations is provided. Moore–Penrose inverse is introduced and its existence and uniqueness is established.
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Miscellaneous Topics,singular values. Reduced normal equations are described and applied to the case of design of experiments model. Properties of the .-matrix are discussed. The E-, A- and D-optimality are defined and the balanced incomplete block design (BIBD) is shown to be optimal according to these criteria.
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