Whenever I teach linear algebra, I suspect many of my students lack the mathematical experience and breadth to appreciate the power and beauty of the subject. So I am always on the hunt for a book that will give them a thorough introduction to linear algebra, but one that will also serve as a good reference as they move on to more advanced mathematics courses. The third edition of Linear Algebra: Algorithms, Applications and Techniques presents linear algebra in an accessible and rigorous manner. This text contains the material found in a standard first linear algebra course. The book is easy to read and includes nice graphs connecting algebraic and geometric ideas. There are several appendices, including one on Jordan Canonical Forms and one on mathematical induction. There’s also a brief appendix to motivate and guide the reader to useful technology. The beginning of the first chapter makes matrix algebra concrete by connecting it to a store’s inventory. This is a nice way to connect to most readers’ experiences.
The authors have made every effort to make this book as easy for students to use as possible. Theorems and computational methods are boxed and easy to find. Some definitions are boxed and some terms are italicized in the text with the definition repeated in blue in the margin. Throughout there are notes in the margin to highlight important ideas. The computational processes are summarized, and then followed by clearly worked examples that include the computational steps as well as a verbal explanation of each step.
All chapters start with an outline which includes page numbers. Each section is concluded with a fair number of exercises which start out as fairly routine but become progressively more demanding. Each chapter has a summary of important concepts along with the section in which they appeared. This is a well-organized textbook that intends to aid a student as much as possible. It strikes me as an excellent book for a first linear algebra course that students would likely also find useful as a reference as they advance through the mathematics curriculum.
Suzanne Caulk is an Associate Professor of Mathematics at Regis University in Denver, CO. She is very interested in modular forms and mathematics education.