Mathematical Tools for Applied Multivariate Analysis, Revised Edition

1st Edition

Editors: Anil Chaturvedi
Authors: J. Carroll Paul Green
Hardcover ISBN: 9780121609542
eBook ISBN: 9780080535906
Imprint: Academic Press
Published Date: 23rd September 1997
Page Count: 376

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Description

This revised edition presents the relevant aspects of transformational geometry, matrix algebra, and calculus to those who may be lacking the necessary mathematical foundations of applied multivariate analysis. It brings up-to-date many definitions of mathematical concepts and their operations. It also clearly defines the relevance of the exercises to concerns within the business community and the social and behavioral sciences. Readers gain a technical background for tackling applications-oriented multivariate texts and receive a geometric perspective for understanding multivariate methods.

Mathematical Tools for Applied Multivariate Analysis, Revised Edition illustrates major concepts in matrix algebra, linear structures, and eigenstructures geometrically, numerically, and algebraically. The authors emphasize the applications of these techniques by discussing potential solutions to problems outlined early in the book. They also present small numerical examples of the various concepts.

Key Features

@introbul:Key Features @bul:* Provides a technical base for tackling most applications-oriented multivariate texts

  • Presents a geometric perspective for aiding ones intuitive grasp of multivariate methods
  • Emphasizes technical terms current in the social and behavioral sciences, statistics, and mathematics
  • Can be used either as a stand-alone text or a supplement to a multivariate statistics textbook
  • Employs many pictures and diagrams to convey an intuitive perception of matrix algebra concepts
  • Toy problems provide a step-by-step approach to each model and matrix algebra concept
  • Provides solutions for all exercises

Readership

Undergraduate and graduate-level courses in quantitative methods and applied multivariate analysis. These courses include: applied multivariate analysis in statistics departments, introductory applied statistics and statisticaltechniques in psychology departments, sociological research in sociology departments, social statistics and marketing information in marketing departments, and mathematics for economists in economics departments.

Table of Contents

The Nature of Multivariate Data Analysis. Vector and Matrix Operations for Multivariate Analysis. Vector and Matrix Concepts from a Geometric Viewpoint. Linear Transformations from a Geometric Viewpoint. Decomposition of Matrix Transformations: Eigenstructures and Quadratic Forms. Applying the Tools to Multivariate Data.

Appendices: Symbolic Differentiation and Optimization of Multivariable Functions. Linear Equations and Generalized Inverses. Answers to Numerical Problems. References. Index.

Details

No. of pages:
376
Language:
English
Copyright:
© Academic Press 1997
Published:
Imprint:
Academic Press
eBook ISBN:
9780080535906
Hardcover ISBN:
9780121609542

About the Editor

Anil Chaturvedi

Affiliations and Expertise

AT&T Bell Labs, Murray Hill, New Jersey

About the Author

J. Carroll

J. Douglas Carroll is the Board of Governor's Professor of Marketing and Psychology in the Graduate School of Management at Rutgers, the State University of New Jersey. He holds a Ph.D. in mathematics from Princeton University. Dr. Carroll has published widely on multidimensional scaling and related techniques of data analysis. He is a member of several professional organizations.

Affiliations and Expertise

Rutgers University, New Brunswick, New Jersey, U.S.A.

Paul Green

Affiliations and Expertise

La Jolla Institute for Allergy and Immunology, La Jolla, California, U.S.A.

Reviews

@qu:"This revision includes an update of terminology and basic mathematical concepts necessitated by the increasing use of multivariate techniques in a wide range of applied fields. It is highly recommended as a companion text for courses in multivariate methods and theory." @source:--JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION @qu:"[The book's] approach is unique and should be an interesting and effective way to learn basic linear algebra, even for some who are primarily interested in linear algebra for its own sake." @source:--CHOICE @qu:"It provides a careful and thorough introduction to vectors and matrices. Especially valuable is the material providing geometric interpretations... A particular strength of the book is the frequent use of small numberical examples which, for example, actually demonstrate the useful properties of determinants, and make absolutely clear what is meant by operations like the multiplication of matrices. The book is designed for readers who have no prior knowledge of matrix theory, and specifically for students in the behavioural and administrative sciences. However, it is also very clear and useful that it has material of value to anyone using multivariate methods. It should be on the reading list for all courses on multivariate analysis." @source:--B.J.T. Morgan, University of Kent, Canterbury, U.K. in SHORT BOOK REVIEWS, December 1998