Matrix algebra is a crucial tool in statistics and many other fields. It is essential for understanding and applying concepts in linear statistical models and multivariate analysis. This book provides a comprehensive overview of matrix algebra tailored for statisticians and others interested in statistical applications. It covers fundamental topics such as matrices, submatrices, linear dependence, linear spaces, determinants, linear systems, generalized inverses, and more. The book also includes advanced topics like eigenvalues, eigenvectors, and linear transformations. It is written in a way that is accessible to readers with a basic understanding of matrix algebra, and it includes detailed proofs and discussions of various results. The book is self-contained and includes exercises with solutions. It serves as both a reference and a textbook for courses on linear statistical models and matrix algebra. The content is organized into 22 chapters, with each chapter containing sections and subsections. The book avoids complex mathematical notation and uses terminology that is more familiar to non-mathematicians. It also includes discussions on matrix differentiation, Kronecker products, and other non-standard topics relevant to statistics. The book is intended for statisticians and professionals in related fields, and it provides a thorough and systematic treatment of matrix algebra with a focus on its applications in statistics.Matrix algebra is a crucial tool in statistics and many other fields. It is essential for understanding and applying concepts in linear statistical models and multivariate analysis. This book provides a comprehensive overview of matrix algebra tailored for statisticians and others interested in statistical applications. It covers fundamental topics such as matrices, submatrices, linear dependence, linear spaces, determinants, linear systems, generalized inverses, and more. The book also includes advanced topics like eigenvalues, eigenvectors, and linear transformations. It is written in a way that is accessible to readers with a basic understanding of matrix algebra, and it includes detailed proofs and discussions of various results. The book is self-contained and includes exercises with solutions. It serves as both a reference and a textbook for courses on linear statistical models and matrix algebra. The content is organized into 22 chapters, with each chapter containing sections and subsections. The book avoids complex mathematical notation and uses terminology that is more familiar to non-mathematicians. It also includes discussions on matrix differentiation, Kronecker products, and other non-standard topics relevant to statistics. The book is intended for statisticians and professionals in related fields, and it provides a thorough and systematic treatment of matrix algebra with a focus on its applications in statistics.