Table of Contents

Preface
Foreword to the Instructor
Foreword to the Student

Chapter 1. Vectors and Matrices
1. Vectors
2. Dot Product
3. Hyperplanes in Rn
4. Systems of Linear Equations and Gaussian Elimination
5. The Theory of Linear Systems
6. Some Applications

Chapter 2. Matrix Algebra
1. Matrix Operations
2. Linear Transformations: An Introduction
3. Inverse Matrices
4. Elementary Matrices: Rows get Equal Time
5. The Transpose

Chapter 3. Vector Spaces
1. Subspaces of Rn
2. The Four Fundamental Subspaces
3. Linear Independence and Basis
4. Dimension and Its Consequences
5. A Graphic Example
6. Abstract Vector Spaces

Chapter 4. Projections and Linear Transformations
1. Inconsistent Systems and Projection
2. Orthogonal Bases
3. The Matrix of a Linear Transformation and the Change-of-Basis Formula
4. Linear Transformations on Abstract Vector Spaces

Chapter 5. Determinants
1. Properties of Determinants
2. Cofactors and Cramer’s Rule
3. Signed Area in R2 and Signed Volume in R2

Chapter 6. Eigenvalues and Eigenvectors
1. The Characteristic Polynomial
2. Diagonalizability
3. Applications
4. The Spectral Theorem

Chapter 7. Further Topics
1. Complex Eigenvalues and Jordan Canonical Form
2. Computer Graphics and Geometry
3. Matrix Exponentials and Differential Equations

For Further Reading
Answers to Selected Exercises
List of Blue Boxes
Index