Matrix Algebra for Engineers

This is a course in matrix algebra, with a focus on concepts that are often used in probability and statistics. Matrix algebra is one of the most important areas of mathematics for data analysis and for statistical theory.

It serves as a complete introduction to matrix algebra, requiring no background knowledge beyond basic school algebra. It begins with the basic definitions and goes on to explain elementary manipulations and the concept of linear dependence, eigenvalues, and eigenvectors - supplying illustrations through fully-worked examples.

It presents the relevant aspects of the theory of matrix algebra for applications in probability and statistics. It moves on to consider the various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. Finally, it covers factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors, etc.

This book could be used as a text for a course in matrices for statistics … or, more generally, a course in statistical computing or linear models. It can be a useful reference book for such a course or, more generally, as a reference for any statistician who uses matrix algebra extensively.