Offering the most geometric presentation available, Linear Algebra with Applications, Fourth Edition emphasizes linear transformations as a unifying theme. This elegant textbook combines a user-friendly presentation with straightforward, lucid language to clarify and organize the many techniques and applications of linear algebra. Exercises and examples make up the heart of the text, with abstract exposition kept to a minimum. Extensive problem sets keep students involved in the material, while genuine applications for a broad range of sciences prepares them for the methods and models of contemporary scientists. In addition, the wealth and variety of exercise sets enable instructors to design a course to best suit the goals and needs of their students. This revision reflects careful review and appropriate changes to the wording of each idea, while preserving the content structure of the previous edition.