This new edition of "Matrix Methods" emphasizes applications to Jordan-canonical forms, differential equations, and least squares. The revision now includes an entire new chapter on inner products, additional material on elementary row applications, and hundreds of new exercises. It provides an introduction to the functional approach to programming. It emphasizes the problem to be solved, not the programming language. It takes the view that all computer programs are a definition of a function. It includes exercises for each chapter. It requires at least a high school algebra level of mathematical sophistication. It is a self-contained work. It can be used as a pre-programming language introduction to the mathematics of computing.