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eBay-Artikelnr.:266909858956
Artikelmerkmale
- Artikelzustand
- Brand
- Unbranded
- Book Title
- Matrix Algebra: Theory, Computations and Applications in Statist
- MPN
- Does not apply
- ISBN
- 9783319648668
Über dieses Produkt
Product Identifiers
Publisher
Springer International Publishing A&G
ISBN-10
3319648667
ISBN-13
9783319648668
eBay Product ID (ePID)
239569774
Product Key Features
Number of Pages
Xxix, 648 Pages
Language
English
Publication Name
Matrix Algebra : Theory, Computations and Applications in Statistics
Publication Year
2017
Subject
Mathematical & Statistical Software, Probability & Statistics / General, Matrices, Algebra / General
Type
Textbook
Subject Area
Mathematics, Computers
Series
Springer Texts in Statistics Ser.
Format
Trade Paperback
Dimensions
Item Weight
44.9 Oz
Item Length
10 in
Item Width
7 in
Additional Product Features
Edition Number
2
Dewey Edition
23
Reviews
"Gentle has put in a lot of time and effort to writing this book with careful attention to details. ... it is all needed to make sure the student has a firm and solid understanding of matrix algebra on the graduate level. I would recommend this book for all those who teach graduate level matrix algebra or ... to those undergraduate students who wish to have an independent study." (Peter Olszewski, MAA Reviews, January, 2018) "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 these methods in practical problem solving." (Stan Lipovetsky, Technometrics, Vol. 60 (2), 2018), "Gentle has put in a lot of time and effort to writing this book with careful attention to details. ... it is all needed to make sure the student has a firm and solid understanding of matrix algebra on the graduate level. I would recommend this book for all those who teach graduate level matrix algebra or ... to those undergraduate students who wish to have an independent study." (Peter Olszewski, MAA Reviews, January 2018)
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
512.9434
Table Of Content
Part I Linear Algebra.- 1 Basic Vector/Matrix Structure and Notation.- 2 Vectors and Vector Spaces.- 3 Basic Properties of Matrices.- 4 Vector/Matrix Derivatives and Integrals.- 5 Matrix Transformations and Factorizations.- 6 Solution of Linear Systems.- 7 Evaluation of Eigenvalues and Eigenvectors.- Part II Applications in Data Analysis.- 8 Special Matrices and Operations Useful in Modeling andData Analysis.- 9 Selected Applications in Statistics.- Part III Numerical Methods and Software.- 10 Numerical Methods.- 11 Numerical Linear Algebra.- 12 Software for Numerical Linear Algebra.- Appendices and Back Matter.- Bibliography.- Index.
Synopsis
This much-needed work presents, among other things, the relevant aspects of the theory of matrix algebra for applications in statistics. Written in an informal style, it addresses computational issues and places more emphasis on applications than existing texts., 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, 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, Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory. The first part of this book presents the relevant aspects of the theory of matrix algebra for applications in statistics. This part begins with the fundamental concepts of vectors and vector spaces, next covers the basic algebraic properties of matrices, then describes the analytic properties of vectors and matrices in the multivariate calculus, and finally discusses operations on matrices in solutions of linear systems and in eigenanalysis. This part is essentially self-contained. The second part of the book begins with a consideration of various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. The second part also describes some of the many applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. The brief coverage in this part illustrates the matrix theory developed in the first part of the book. The first two parts of the book can be used as the text 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 of this book covers numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting 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/S-Plus or Matlab. This part of the book can be used as the text for a course in statistical computing, or as a supplementary text for various courses that emphasize computations. The book includes a large number of exercises with some solutions provided in an appendix.
LC Classification Number
QA276-280
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