Mathematical Tools for Applied Multivariate Analysis

ISBN-13: 9780121609559 / Angielski / Miękka / 1997 / 376 str.

J. Douglas Carroll; Douglas Green; Anil Chaturvedi

Opis

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.

• 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

Recenzje

"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." --JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION

"[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." --CHOICE

"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 numerical 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." --B.J.T. Morgan, Univeristy of Kent, Canterbury, U.K. in SHORT BOOK REVIEWS, December 1998

Spis treści

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

O autorze

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.