Springer Texts in Statistics

Matrix Algebra

Theory, Computations and Applications in Statistics

Authors: Gentle, James E.

  • A hugely important work for statisticians, the book’s emphasis is on the areas of matrix analysis that are key sectors for this group of people
  • Practical use: includes a large number of exercises with some solutions provided in an appendix
  • Relevant in all the right areas, this book addresses computational issues as well as placing more emphasis on applications than existing texts
  • Written in an informal style that makes the book’s complex material accessible
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Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-319-64867-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-319-64866-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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

About the authors

​James E. Gentle, PhD, is University Professor of Computational Statistics at George Mason University. He is a Fellow of the American Statistical Association (ASA) and of the American Association for the Advancement of  Science. Professor Gentle has held several national offices in the ASA and has served as editor and associate editor of journals of the ASA as well as for other journals in statistics and computing. He is author of Random Number Generation and Monte Carlo Methods (Springer, 2003) and Computational Statistics (Springer, 2009).

Table of contents (12 chapters)

  • Basic Vector/Matrix Structure and Notation

    Gentle, James E.

    Pages 3-10

  • Vectors and Vector Spaces

    Gentle, James E.

    Pages 11-54

  • Basic Properties of Matrices

    Gentle, James E.

    Pages 55-183

  • Vector/Matrix Derivatives and Integrals

    Gentle, James E.

    Pages 185-225

  • Matrix Transformations and Factorizations

    Gentle, James E.

    Pages 227-263

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-319-64867-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-319-64866-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Matrix Algebra
Book Subtitle
Theory, Computations and Applications in Statistics
Authors
Series Title
Springer Texts in Statistics
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-64867-5
DOI
10.1007/978-3-319-64867-5
Softcover ISBN
978-3-319-64866-8
Series ISSN
1431-875X
Edition Number
2
Number of Pages
XXIX, 648
Number of Illustrations and Tables
40 b/w illustrations
Topics