Mathematical Tools for Applied Multivariate AnalysisMathematical 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. |
Contents
| 1 | |
| 26 | |
CHAPTER 3 Vector and Matrix Concepts from a Geometric Viewpoint | 77 |
CHAPTER 4 Linear Transformations from a Geometric Viewpoint | 127 |
Eigenstructures and Quadratic Forms | 194 |
CHAPTER 6 Applying the Tools to Multivariate Data | 259 |
Symbolic Differentiation and Optimization of Multivariable Functions | 295 |
Linear Equations and Generalized inverses | 323 |
Answers to Numerical Problems | 352 |
| 364 | |
| 369 | |
Other editions - View all
Mathematical Tools for Applied Multivariate Analysis J. Douglas Carroll,Paul E. Green,Anil Chaturvedi No preview available - 1997 |
Mathematical Tools for Applied Multivariate Analysis J. Douglas Carroll,Paul E. Green,Anil Chaturvedi No preview available - 1997 |
Common terms and phrases
angle applied axes axis basic structure basis vectors Chapter coefficients column vector compute concept coordinates covariance matrix data matrix defined denotes described determinant diagonal matrix dimensions discussion echelon form eigenvalues eigenvectors elementary row operations entries equal example finding the eigenstructure function geometric Hence Hermite form identity matrix illustrated involving linear combination linear composite linear equations linear transformation linearly independent matrix algebra matrix inversion matrix rank matrix transformations mean-corrected multiple discriminant analysis multiple regression multivariate analysis multivariate techniques nonsingular nonsymmetric obtained orthogonal matrix orthonormal Panel pivotal method point transformation predictor variables principal components analysis procedure properties quadratic forms rectangular represented row vector sample problem scalar product scores Section set of simultaneous shown simultaneous equations solution space SSCP matrix stationary point stretch subtraction sums of squares symmetric matrix Table transformation matrix transpose unit length values variance within-group X1 and X2 zero