Linear algebra and the study of matrix algorithms have become fundamental to the development of statistical models. Using a vector space approach, this book provides an understanding of the major concepts that underlie linear algebra and matrix analysis. Each chapter introduces a key topic such as infinite-dimensional spaces and provides illustrative examples. The author examines recent developments in diverse fields such as spatial statistics, machine learning, data mining and social network analysis. Complete in its coverage and accessible to students without prior knowledge of linear algebra, the text also includes results that are useful for traditional statistical applications.