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Mathematical Tools for Applied Multivariate Analysis

  • ID: 1767893
  • Book
  • October 1997
  • 376 Pages
  • Elsevier Science and Technology
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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

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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.
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Carroll, J. Douglas
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.
Green, Paul
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