# Table of Contents

### Chapter 1: What is Linear Algebra?

### Chapter 2: Systems of Linear Equations

### Chapter 3: The Simplex Method

### Chapter 4: Vectors in Space, n-Vectors

### Chapter 5: Vector Spaces

### Chapter 6: Linear Transformations

### Chapter 7: Matrices

### Chapter 8: Determinants

### Chapter 9: Subspaces and Spanning Sets

### Chapter 10: Linear Independence

### Chapter 11: Basis and Dimension

### Chapter 12: Eigenvalues and Eigenvectors

### Chapter 13: Diagonalization

### Chapter 14: Orthonormal Bases and Complements

### Chapter 15: Diagonalizing Symmetric Matrices

### Chapter 16: Kernel, Range, Nullity, Rank

### Chapter 17: Least Squares and Singular Values

### Appendices: Symbols, Fields, Sample Exams, Online Resources, Movie Scripts

### Index