Matrix Algebra

Theory, Computations and Applications in Statistics

  • James E. Gentle

Part of the Springer Texts in Statistics book series (STS)

Table of contents

  1. Front Matter
    Pages i-xxix
  2. Linear Algebra

    1. Front Matter
      Pages 1-1
    2. James E. Gentle
      Pages 3-10
    3. James E. Gentle
      Pages 11-54
    4. James E. Gentle
      Pages 55-183
    5. James E. Gentle
      Pages 185-225
    6. James E. Gentle
      Pages 227-263
    7. James E. Gentle
      Pages 265-306
    8. James E. Gentle
      Pages 307-325
  3. Applications in Data Analysis

    1. Front Matter
      Pages 327-327
    2. James E. Gentle
      Pages 399-458
  4. Numerical Methods and Software

    1. Front Matter
      Pages 459-459
    2. James E. Gentle
      Pages 461-521
    3. James E. Gentle
      Pages 523-538
    4. James E. Gentle
      Pages 539-585
  5. Back Matter
    Pages 587-648

About this book

Introduction

This textbook for graduate and advanced undergraduate students presents the theory of matrix algebra for statistical applications, explores various types of matrices encountered in statistics, and covers numerical linear algebra. Matrix algebra is one of the most important areas of mathematics in data science and in statistical theory, and the second edition of this very popular textbook provides essential updates and comprehensive coverage on critical topics in mathematics in data science and in statistical theory.

Part I offers a self-contained description of relevant aspects of the theory of matrix algebra for applications in statistics. It begins with fundamental concepts of vectors and vector spaces; covers basic algebraic properties of matrices and analytic properties of vectors and matrices in multivariate calculus; and concludes with a discussion on operations on matrices in solutions of linear systems and in eigenanalysis. Part II considers various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes special properties of those matrices; and describes various applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. Part III covers numerical linear algebra—one of the most important subjects in the field of statistical computing. It begins with a discussion of the basics of numerical computations and goes on to describe accurate and efficient algorithms for factoring matrices, how to solve linear systems of equations, and the extraction of eigenvalues and eigenvectors.

Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. This part is essentially self-contained, although it assumes some ability to program in Fortran or C and/or the ability to use R or Matlab.

The first two parts of the text are ideal for a course in matrix algebra for statistics students or as a supplementary text for various courses in linear models or multivariate statistics. The third part is ideal for use as a text for a course in statistical computing or as a supplementary text for various courses that emphasize computations.

New to this edition

• 100 pages of additional material

• 30 more exercises—186 exercises overall
• Added discussion of vectors and matrices with complex elements
• Additional material on statistical applications
• Extensive and reader-friendly cross references and index

Keywords

matrix linear algebra numerical analysis optimization linear model vector linear transformation singular value decomposition generalized inverse determinant eigenvalue eigenvector graph theory linear system positive definite R software vector space inner product geometry

Authors and affiliations

  • James E. Gentle
    • 1
  1. 1.FairfaxUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-64867-5
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-64866-8
  • Online ISBN 978-3-319-64867-5
  • Series Print ISSN 1431-875X
  • Series Online ISSN 2197-4136
  • About this book