Offering the most geometric presentation available, Linear Algebra with Applications, Fifth 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 techniques and applications of linear algebra. Exercises and examples make up the heart of the text, with abstract exposition kept to a minimum. Exercise sets are broad and varied and reflect the author’s creativity and passion for this course. This revision reflects careful review and appropriate edits throughout, while preserving the order of topics of the previous edition.
1. A large number of exercises have been added to the problem sets, from the elementary to the challenging and from the abstract to the applied. For example, there are quite a few new exercises on “Fibonacci Matrices” and their eigenvectors and eigenvalues.
2. Throughout the text, the author added an ongoing discussion of the mathematical principles behind search engines—and the notion of PageRank in particular—with dozens of examples and exercises. Besides being an interesting and important contemporary application of linear algebra, this topic allows for an early and meaningful introduction to dynamical systems, one of the main themes of this text, naturally leading up to a discussion of diagonalization and eigenvectors.
3. A new appendix offers a brief discussion of the proof techniques of Induction and Contraposition.
4. Hundreds of improvements, such as offering hint in a challenge problem, for example, or choosing a more sensible notation in a definition.