Mathematical Tools for Applied Multivariate Analysis

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 textsPresents a geometric perspective for aiding ones intuitive grasp of multivariate methodsEmphasizes technical terms current in the social and behavioral sciences, statistics, and mathematicsCan be used either as a stand-alone text or a supplement to a multivariate statistics textbookEmploys many pictures and diagrams to convey an intuitive perception of matrix algebra conceptsToy problems provide a step-by-step approach to each model and matrix algebra conceptProvides solutions for all exercises

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.