Mathematical Tools for Applied Multivariate Analysis

This book introduces matrix algebra to students in behavioral and administrative sciences. It clearly defines the relevance of the exercises to concerns within the business community and the social and behavioral sciences. Readers will gain a technical background for tackling applications-oriented multivariate texts. Mathematical Tools for Applied Multivariate Analysis provides information pertinent to the aspects of transformational geometry, matrix algebra, and the calculus that are most relevant for the study of multivariate analysis. This book discusses the mathematical foundations of applied multivariate analysis. Organized into six chapters, this book begins with an overview of the three problems in multiple regression, principal components analysis, and multiple discriminant analysis. This text then presents a standard treatment of the mechanics of matrix algebra, including definitions and operations on matrices, vectors, and determinants. Other chapters consider the topics of eigenstructures and linear transformations that are important to the understanding of multivariate techniques. This book discusses as well the eigenstructures and quadratic forms. The final chapter deals with the geometric aspects of linear transformations. This book is a valuable resource for students. Content: Front Matter, Page iii Copyright, Page v Dedication, Page vi Preface, Pages xi-xii Acknowledgements, Page xiii CHAPTER 1 - The Nature of Multivariate Data Analysis, Pages 1-25 CHAPTER 2 - Vector and Matrix Operations for Multivariate Analysis, Pages 26-76 CHAPTER 3 - Vector and Matrix Concepts from a Geometric Viewpoint, Pages 77-126 CHAPTER 4 - Linear Transformations from a Geometric Viewpoint, Pages 127-193 CHAPTER 5 - Decomposition of Matrix Transformations: Eigenstructures and Quadratic Forms, Pages 194-258 CHAPTER 6 - Applying the Tools to Multivariate Data, Pages 259-294 APPENDIX A - Symbolic Differentiation and Optimization of Multivariable Functions, Pages 295-322 APPENDIX B - Linear Equations and Generalized Inverses, Pages 323-351 Answers to Numerical Problems, Pages 352-363 References, Pages 364-367 Index, Pages 369-376 Paul E. Green, With Contributions By J. Douglas Carroll. Includes Index. Bibliography: P. 364-367.