Matrix Algebra for Linear Models

<p><b>A self-contained introduction to matrix analysis theory and applications in the field of statistics</b></p> <p>Comprehensive in scope, <i>Matrix Algebra for Linear Models</i> offers a succinct summary of matrix theory and its related applications to statistics, especially linear models. The book provides a unified presentation of the mathematical properties and statistical applications of matrices in order to define and manipulate data.</p> <p>Written for theoretical and applied statisticians, the book utilizes multiple numerical examples to illustrate key ideas, methods, and techniques crucial to understanding matrix algebra’s application in linear models. <i>Matrix Algebra for Linear Models</i> expertly balances concepts and methods allowing for a side-by-side presentation of matrix theory and its linear model applications. Including concise summaries on each topic, the book also features:</p> <ul> <li>Methods of deriving results from the properties of eigenvalues and the singular value decomposition</li> <li>Solutions to matrix optimization problems for obtaining more efficient biased estimators for parameters in linear regression models</li> <li>A section on the generalized singular value decomposition</li> <li>Multiple chapter exercises with selected answers to enhance understanding of the presented material</li> </ul> <p><i>Matrix Algebra for Linear Models</i> is an ideal textbook for advanced undergraduate and graduate-level courses on statistics, matrices, and linear algebra. The book is also an excellent reference for statisticians, engineers, economists, and readers interested in the linear statistical model.</p>