Otto Bretscher-Colby College. Waterville

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"

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.