Matrix Algebra Useful for Statistics, 2nd Edition

A thoroughly updated guide to matrix algebra and it uses in statistical analysis and features SAS®, MATLAB®, and R throughout

This Second Edition addresses matrix algebra that is useful in the statistical analysis of data as well as within statistics as a whole. The material is presented in an explanatory style rather than a formal theorem-proof format and is self-contained. Featuring numerous applied illustrations, numerical examples, and exercises, the book has been updated to include the use of SAS, MATLAB, and R for the execution of matrix computations. In addition, André I. Khuri, who has extensive research and teaching experience in the field, joins this new edition as co-author. The Second Edition also:

• Contains new coverage on vector spaces and linear transformations and discusses computational aspects of matrices
• Covers the analysis of balanced linear models using direct products of matrices
• Analyzes multiresponse linear models where several responses can be of interest
• Includes extensive use of SAS, MATLAB, and R throughout
• Contains over 400 examples and exercises to reinforce understanding along with select solutions
• Includes plentiful new illustrations depicting the importance of geometry as well as historical interludes

Matrix Algebra Useful for Statistics, Second Edition is an ideal textbook for advanced undergraduate and first-year graduate level courses in statistics and other related disciplines. The book is also appropriate as a reference for independent readers who use statistics and wish to improve their knowledge of matrix algebra.

THE LATE SHAYLE R. SEARLE, PHD, was professor emeritus of biometry at Cornell University. He was the author of Linear Models for Unbalanced Data and Linear Models and co-author of Generalized, Linear, and Mixed Models, Second Edition, Matrix Algebra for Applied Economics, and Variance Components, all published by Wiley. Dr. Searle received the Alexander von Humboldt Senior Scientist Award, and he was an honorary fellow of the Royal Society of New Zealand.

ANDRÉ I. KHURI, PHD, is Professor Emeritus of Statistics at the University of Florida. He is the author of Advanced Calculus with Applications in Statistics, Second Edition and co-author of Statistical Tests for Mixed Linear Models, all published by Wiley. Dr. Khuri is a member of numerous academic associations, among them the American Statistical Association and the Institute of Mathematical Statistics.

Table of Contents

PART I DEFINITIONS, BASIC CONCEPTS, AND MATRIX OPERATIONS
Chapter 1 Vector Spaces, Subspaces, And Linear Transformations
Chapter 2 Matrix Notation And Terminology
Chapter 3 Determinants
Chapter 4 Matrix Operations
Chapter 5 Special Matrices
Chapter 6 Eigenvalues And Eigenvectors
Chapter 7 Diagonalization Of Matrices
Chapter 8 Generalized Inverses
Chapter 9 Matrix Calculus

PART II APPLICATIONS OF MATRICES IN STATISTICS
Chapter 10 Multivariate Distributions And Quadratic Forms
Chapter 11 Matrix Algebra Of Full-Rank Linear Models
Chapter 12 Less-Than-Full-Rank Linear Models
Chapter 13 Analysis Of Balanced Linear Models Using Direct Products Of Matrices
Chapter 14 Multiresponse Models

PART III MATRIX COMPUTATIONS AND RELATED SOFTWARE
Chapter 15 Sas/Iml
Chapter 16 Use Of Matlab In Matrix Computations
Chapter 17 Use Of R In Matrix Computations