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Linear Algebra and Linear Models

  • R.B. Bapat

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. R. B. Bapat
    Pages 1-8
  3. R. B. Bapat
    Pages 31-36
  4. R. B. Bapat
    Pages 61-77
  5. R. B. Bapat
    Pages 79-98
  6. R. B. Bapat
    Pages 99-114
  7. R. B. Bapat
    Pages 115-128
  8. R. B. Bapat
    Pages 129-134
  9. R. B. Bapat
    Pages 135-156
  10. R. B. Bapat
    Pages 157-159
  11. Back Matter
    Pages 161-167

About this book

Introduction

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.

Keywords

linear algebra linear model mixed effects model normal equations variance components variance-covariance matrix

Authors and affiliations

  • R.B. Bapat
    • 1
  1. 1.Indian Statistical InstituteNew DelhiIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-2739-0
  • Copyright Information Springer-Verlag London Limited 2012
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-2738-3
  • Online ISBN 978-1-4471-2739-0
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site