Matrix Algebra for Linear Models

A self-contained introduction to matrix analysis theory and applications in the field of statistics Comprehensive in scope, Matrix Algebra for Linear Models 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. 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. Matrix Algebra for Linear Models 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: Methods of deriving results from the properties of eigenvalues and the singular value decomposition Solutions to matrix optimization problems for obtaining more efficient biased estimators for parameters in linear regression models A section on the generalized singular value decomposition Multiple chapter exercises with selected answers to enhance understanding of the presented material Matrix Algebra for Linear Models 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.

A self-contained introduction to matrix analysis theory andapplications in the field of statisticsComprehensive in scope, Matrix Algebra for Linear Modelsoffers a succinct summary of matrix theory and its relatedapplications to statistics, especially linear models. The bookprovides a unified presentation of the mathematical properties andstatistical applications of matrices in order to define andmanipulate data.Written for theoretical and applied statisticians, the bookutilizes multiple numerical examples to illustrate key ideasmethods, and techniques crucial to understanding matrixalgebra's application in linear models. Matrix Algebra forLinear Models expertly balances concepts and methods allowingfor a side-by-side presentation of matrix theory and its linearmodel applications. Including concise summaries on each topic, thebook also features:* Methods of deriving results from the properties of eigenvaluesand the singular value decomposition* Solutions to matrix optimization problems for obtaining moreefficient biased estimators for parameters in linear regressionmodels* A section on the generalized singular value decomposition* Multiple chapter exercises with selected answers to enhanceunderstanding of the presented materialMatrix Algebra for Linear Models is an ideal textbook foradvanced undergraduate and graduate-level courses on statisticsmatrices, and linear algebra. The book is also an excellentreference for statisticians, engineers, economists, and readersinterested in the linear statistical model.