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