| Introductory Linear Algebra / I： |
| Linear Equations and Matrices / 1： |
| Linear Systems |
| Matrices |
| Dot Product and Matrix Multiplication |
| Properties of Matrix Operations |
| Graph Theory (Optional) |
| Solutions of Linear Systems of Equations |
| Electrical Circuits (Optional) |
| Markov Chains (Optional) |
| The Inverse of a Matrix |
| Linear Economic Models (Optional) |
| Wavelets (Optional) |
| LU-Factorization (Optional) |
| Determinants / 2： |
| Definition and Properties |
| Cofactor Expansion and Applications |
| Determinants from a Computational Point of View |
| Vectors in R2 and R3 / 3： |
| Vectors in the Plane |
| N-Vectors |
| Introduction to Linear Transformations |
| Computer Graphics |
| Computer Graphics (Optional) |
| Cross Products in R3 (Optional) |
| Lines and Planes |
| Real Vector Spaces / 4： |
| Subspaces |
| Linear Independence |
| Basis and Dimension |
| Homogeneous Systems |
| The Rank of a Matrix and Applications |
| Coordinates and Change of Basis |
| Orthonormal Bases in Rn |
| QR-Factorization (Optional) |
| Orthogonal Complements |
| Least Squares (Optional) |
| Eigenvalues and Eigenvectors / 5： |
| Diagonalization and Similar Matrices |
| Diagonalization and Symmetric Matrices |
| Linear Transformations and Matrices / 6： |
| Definition and Examples |
| The Kernel and Range of a Linear Transformation |
| The Matrix of a Linear Transformation |
| Cumulative Review of Part I |
| OTHER APPLICATIONS / II： |
| Linear Programming / 7： |
| The Linear Programming Problem |
| Geometric Solution |
| The Simplex Method |
| Duality |
| The Theory of Games |
| Applications of Eigenvalues and Eigenvectors / 8： |
| The Fibonacci Sequence |
| Differential Equations (Calculus Required) |
| Dynamical Systems (Calculus Required) |
| Intro to Fractals |
| Quadratic Forms |
| Conic Sections |
| Quadric Surfaces |
| Introduction to MATLAB / Appendix A： |
| Complex Numbers / Appendix B： |
| Complex Numbers in Linear Algebra |
| Further Directions / Appendix C： |
| Inner Product Spaces (Calculus Required) |
| Composite and Invertible Linear Transformations |
| Answers to Odd-Numbered Exercises and Chapter Tests |
| Index |
| Introductory Linear Algebra / I： |
| Linear Equations and Matrices / 1： |
| Linear Systems |
| Matrices |
| Dot Product and Matrix Multiplication |
| Properties of Matrix Operations |
