Overview
- Comprehensive coverage of matrix algebra for data science and statistical theory
- Over 100 pages of additional material and 30 extra exercises in the new edition
- Even clearer text and more comprehensive coverage
- Includes supplementary material: sn.pub/extras
Part of the book series: Springer Texts in Statistics (STS)
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Table of contents (12 chapters)
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Front Matter
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Applications in Data Analysis
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Front Matter
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Numerical Methods and Software
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Front Matter
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Back Matter
Keywords
About this book
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 matricesencountered 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
Reviews
“Beautifully written, easy to read, with a well subindexed index of 16 pages and a bibliography of 13 that includes most modern and relevant textbooks and articles in the area of matrix theory and computations, as well as for statistics and big data computations.” (Frank Uhlig, zbMATH 1386.15002, 2018)
“This very reader-friendly written volume presents an opportunity to graduate students and researchers to enjoy reading on the classical matrix analysis in its modern applications to statistics and to implement thesemethods in practical problem solving.” (Stan Lipovetsky, Technometrics, Vol. 60 (2), 2018)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Matrix Algebra
Book Subtitle: Theory, Computations and Applications in Statistics
Authors: James E. Gentle
Series Title: Springer Texts in Statistics
DOI: https://doi.org/10.1007/978-3-319-64867-5
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-64866-8Published: 21 October 2017
eBook ISBN: 978-3-319-64867-5Published: 12 October 2017
Series ISSN: 1431-875X
Series E-ISSN: 2197-4136
Edition Number: 2
Number of Pages: XXIX, 648
Number of Illustrations: 40 b/w illustrations
Topics: Statistical Theory and Methods, Algebra, Statistics and Computing/Statistics Programs, Probability and Statistics in Computer Science, Computational Mathematics and Numerical Analysis, Numeric Computing