| Systems of Linear Equations and Matrices |
| Note: All relevant chapters end with Supplementary Exercises. |
| Determinants |
| Vectors in 2-Space and 3-Space / 1： |
| Linear Equations and Matrices |
| Euclidean Vector Spaces |
| Systems of Linear Equations |
| General Vector Spaces |
| Matrices |
| Inner Product Spaces |
| Matrix Multiplication |
| Eigenvalues, Eigenvectors |
| Algebraic Properties of Matrix Operations |
| Linear Transformations |
| Special Types of Matrices and Partitioned Matrices |
| Additional Topics |
| Matrix Transformations |
| Complex Vector Spaces |
| Computer Graphics |
| Answers to Exercises |
| Correlation Coefficient (Optional) |
| Photo Credits |
| Index / 2： |
| Solving Linear Systems |
| Echelon Form of a Matrix |
| Elementary Matrices: Finding A-1 |
| Equivalent Matrices |
| LU-Factorization (Optional) |
| Real Vector Spaces / 3： |
| Vectors in the Plane and in 3-space |
| Vector Spaces |
| Subspaces |
| Span and Linear Independence |
| Basis and Dimension |
| Homogeneous Systems |
| Coordinates and Isomorphisms |
| Rank of a Matrix |
| Standard Inner Product on R2 and R3 / 4： |
| Cross Product in R3 (Optional) |
| Gram-Schmidt Process |
| Orthogonal Complements |
| Least Squares (Optional) |
| Linear Transformations and Matrices / 5： |
| Definition and Examples |
| Kernel and Range of a Linear Transformation |
| Matrix of a Linear Transformation |
| Vector Space of Matrices and Vector Space of Linear Transformations (Optional) |
| Similarity |
| Inroduction to Homogeneous Coordinates (Optional) |
| Definition / 6： |
| Properties of Determinants |
| Cofactor Expansion |
| Inverse of a Matrix |
| Other Applications of Determinants |
| Determinants from a Computational Point of View |
| Eigenvalues and Eigenvectors / 7： |
| Diagonalization and Similar Matrices |
| Stable Age Distribution in a Population |
| Markov Processes (Optional) |
| Diagonalization of Symmetric Matrices |
| Spectral Decomposition and Singular Value Decomposition (Optional) |
| Real Quadratic Forms |
| Conic Sections |
| Quadric Surfaces |
| Dominant Eigenvalue and Principal Component Analysis (Optional) |
| Differential Equations (Optional) / 8： |
| Differential Equations |
| Dynamical Systems |
| MATLAB for Linear Algebra / 9： |
| Input and Output in MATLAB |
| Matrix Operations in MATLAB |
| Matrix Powers and Some Special Matrices |
| Elementary Row Operations in MATLAB |
| Matrix Inverses in MATLAB |
| Vectors in MATLAB |
| Applications of Linear Combinations in MATLAB |
| Linear Transformations in MATLAB |
| MATLAB Command Summary |
| MATLAB Exercises / 10： |
| Preliminaries Sets Functions / Appendix A： |
| Complex Numbers Complex Numbers Complex Numbers in Linear Algebra / Appendix B： |
| Introduction to Proofs / Appendix C： |
| Answers to Odd-Numbered Exercises |
| Systems of Linear Equations and Matrices |
| Note: All relevant chapters end with Supplementary Exercises. |
| Determinants |
| Vectors in 2-Space and 3-Space / 1： |
| Linear Equations and Matrices |
| Euclidean Vector Spaces |
