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.

Chapter 1. Linear Equations
Chapter 2. Linear Transformations
Chapter 3. Subspaces of Rn and Their Dimensions
Chapter 4. Linear Spaces
Chapter 5. Orthogonality and Least Squares
Chapter 6. Determinants
Chapter 7. Eigenvalues and Eigenvectors
Chapter 8. Symmetric Matrices and Quadratic Forms
Chapter 9. Linear Differential Equations"

Salient Features

1. Linear transformations are introduced early in the text to make the discussion of matrix operations more meaningful and easier to navigate.
2. Visualization and geometrical interpretation are emphasized extensively throughout the text.
3. An abundance of problems, exercises, and applications help students assess their understanding and master the material.
4. Abstract concepts are introduced gradually throughout the text. Major ideas are carefully developed at various levels of generality before the student is introduced to abstract vector spaces.
5. Discrete and continuous dynamical systems are used as a motivation for eigenvectors and as a unifying theme thereafter.
6. Fifty to sixty True/False questions conclude every chapter, testing conceptual understanding and encouraging students to read the text.
7. Historical problems from ancient Chinese, Indian, Arabic, and early European sources add diversity to the selection of exercises.
8. Rotations, reflections, projections, and shears are used throughout to illustrate new ideas.
9. Multiple perspectives on the kernel of a matrix are presented, with a stronger emphasis on the relations among the columns.
10. Commutative diagrams enhance students' conceptual understanding of the matrix of a linear transformation. These diagrams enable students to visualize the relations between linear transformations.
11. A more conceptual approach to the QR factorization is presented, in terms of a change-of-basis.