This book emphasizes linear algebra as an experimental science. It provides a balance of applications, theory, and computation, and also examines their interdependence. The text has a strong orientation towards numerical computation and the linear algebra needed in applied mathematics. At the same time, it contains a rigorous and self-contained development of most of the traditional topics in a linear algebra course, making it an ideal textbook for a one or two semester sophomore level course. The book provides background for numerous projects and includes a comprehensive set of exercises.