Overview
- 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 testing in linear models covering the basic results required for further studies in linear models, multivariate analysis and design of experiments
- Contains a large number of exercises, including over seventy five problems on rank, with hints and solutions
- Includes supplementary material: sn.pub/extras
Part of the book series: Universitext (UTX)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (13 chapters)
-
Front Matter
-
Back Matter
Keywords
About this book
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 design of experiments. A wealth of exercises, complete with hints and solutions, help to consolidate understanding. Researchers in mathematics and statistics will also find the book a useful source of results and problems.
Reviews
From the book reviews:
“The author presents basic ideas and concepts of linear algebra and linear models equally from both theoretical and applications perspectives. … This book is well presented and structured for an upper level undergraduate course for students of statistics. Further, it can serve as a textbook for an entry-level graduate course. Not only that, it can act as a reference book for practitioners and research statisticians.” (Technometrics, Vol. 55 (1), August, 2012)
Authors and Affiliations
Bibliographic Information
Book Title: Linear Algebra and Linear Models
Authors: R.B. Bapat
Series Title: Universitext
DOI: https://doi.org/10.1007/978-1-4471-2739-0
Publisher: Springer London
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag London Limited 2012
Softcover ISBN: 978-1-4471-2738-3Published: 29 January 2012
eBook ISBN: 978-1-4471-2739-0Published: 28 January 2012
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 3
Number of Pages: VIII, 167
Number of Illustrations: 1 b/w illustrations
Additional Information: Jointly published with Hindustan Book Agency, New Delhi, India. Originally published by Hindustan Book Agency, New Delhi, India
Topics: Linear and Multilinear Algebras, Matrix Theory, Statistical Theory and Methods, Statistics for Business, Management, Economics, Finance, Insurance
Industry Sectors: IT & Software