Matrix Analysis for Statistics, 3rd Edition

An up-to-date version of the complete, self-contained introduction to matrix analysis theory and practice

Providing accessible and in-depth coverage of the most common matrix methods now used in statistical applications, Matrix Analysis for Statistics, Third Edition features an easy-to-follow theorem/proof format. Featuring smooth transitions between topical coverage, the author carefully justifies the step-by-step process of the most common matrix methods now used in statistical applications, including eigenvalues and eigenvectors; the Moore-Penrose inverse; matrix differentiation; and the distribution of quadratic forms.

An ideal introduction to matrix analysis theory and practice, Matrix Analysis for Statistics, Third Edition features:

• New chapter or section coverage on inequalities, oblique projections, and antieigenvalues and antieigenvectors
• Additional problems and chapter-end practice exercises at the end of each chapter
• Extensive examples that are familiar and easy to understand
• Self-contained chapters for flexibility in topic choice
• Applications of matrix methods in least squares regression and the analyses of mean vectors and covariance matrices

Matrix Analysis for Statistics, Third Edition is an ideal textbook for upper-undergraduate and graduate-level courses on matrix methods, multivariate analysis, and linear models. The book is also an excellent reference for research professionals in applied statistics.

James R. Schott, PhD, is Professor in the Department of Statistics at the University of Central Florida. He has published numerous journal articles in the area of multivariate analysis. Dr. Schott’s research interests include multivariate analysis, analysis of covariance and correlation matrices, and dimensionality reduction techniques.

Table of Contents

Chapter 1 A Review of Elementary Matrix Algebra
Chapter 2 Vector Spaces
Chapter 3 Eigenvalues and Eigenvectors
Chapter 4 Matrix Factorizations and Matrix Norms
Chapter 5 Generalized Inverses
Chapter 6 Systems of Linear Equations
Chapter 7 Partitioned Matrices
Chapter 8 Special Matrices and Matrix Operations
Chapter 9 Matrix Derivatives and Related Topics
Chapter 10 Inequalities
Chapter 11 Some Special Topics Related to Quadratic Forms