| Linear Equations in Linear Algebra / 1： |
| Introductory Example: Linear Models in Economics and Engineering |
| Systems of Linear Equations / 1.1： |
| Row Reduction and Echelon Forms / 1.2： |
| Vector Equations / 1.3： |
| The Matrix Equation Ax = b / 1.4： |
| Solution Sets of Linear Systems / 1.5： |
| Applications of Linear Systems / 1.6： |
| Linear Independence / 1.7： |
| Introduction to Linear Transformations / 1.8： |
| The Matrix of a Linear Transformation / 1.9： |
| Linear Models in Business, Science, and Engineering / 1.10： |
| Supplementary Exercises |
| Matrix Algebra / 2： |
| Introductory Example: Computer Models in Aircraft Design |
| Matrix Operations / 2.1： |
| The Inverse of a Matrix / 2.2： |
| Characterizations of Invertible Matrices / 2.3： |
| Partitioned Matrices / 2.4： |
| Matrix Factorizations / 2.5： |
| The Leontief Input=Output Model / 2.6： |
| Applications to Computer Graphics / 2.7： |
| Subspaces of Rn / 2.8： |
| Dimension and Rank / 2.9： |
| Determinants / 3： |
| Introductory Example: Determinants in Analytic Geometry |
| Introduction to Determinants / 3.1： |
| Properties of Determinants / 3.2： |
| Cramer's Rule, Volume, and Linear Transformations / 3.3： |
| Vector Spaces / 4： |
| Introductory Example: Space Flight and Control Systems |
| Vector Spaces and Subspaces / 4.1： |
| Null Spaces, Column Spaces, and Linear Transformations / 4.2： |
| Linearly Independent Sets Bases / 4.3： |
| Coordinate Systems / 4.4： |
| The Dimension of a Vector Space / 4.5： |
| Rank / 4.6： |
| Change of Basis / 4.7： |
| Applications to Difference Equations / 4.8： |
| Applications to Markov Chains / 4.9： |
| Eigenvalues and Eigenvectors / 5： |
| Introductory Example: Dynamical Systems and Spotted Owls |
| Eigenvectors and Eigenvalues / 5.1： |
| The Characteristic Equation / 5.2： |
| Diagonalization / 5.3： |
| Eigenvectors and Linear Transformations / 5.4： |
| Complex Eigenvalues / 5.5： |
| Discrete Dynamical Systems / 5.6： |
| Applications to Differential Equations / 5.7： |
| Iterative Estimates for Eigenvalues / 5.8： |
| Orthogonality and Least Squares / 6： |
| Introductory Example: Readjusting the North American Datum |
| Inner Product, Length, and Orthogonality / 6.1： |
| Orthogonal Sets / 6.2： |
| Orthogonal Projections / 6.3： |
| The Gram-Schmidt Process / 6.4： |
| Least-Squares Problems / 6.5： |
| Applications to Linear Models / 6.6： |
| Inner Product Spaces / 6.7： |
| Applications of Inner Product Spaces / 6.8： |
| Symmetric Matrices and Quadratic Forms / Chapter 7： |
| Introductory Example: Multichannel Image Processing |
| Diagonalization of Symmetric Matrices / 7.1： |
| Quadratic Forms / 7.2： |
| Constrained Optimization / 7.3： |
| The Singular Value Decomposition / 7.4： |
| Applications to Image Processing and Statistics / 7.5： |
| Supplementary Exercises (ONLINE ONLY) |
| The Geometry of Vector Spaces / 8： |
| Introductory Example: The Platonic Solids |
| Affine Combinations / 8.1： |
| Affine Independence / 8.2： |
| Convex Combinations / 8.3： |
| Hyperplanes / 8.4： |
| Polytopes / 8.5： |
| Curves and Surfaces / 8.6： |
| Optimization / 9： |
| Introductory Example: The Berlin Airlift |
| Matrix Games / 9.1： |
| Linear Programming - Geometric Method / 9.2： |
| Linear Programming - Simplex Method / 9.3： |
| Duality / 9.4： |
| Appendices |
| Uniqueness of the Reduced Echelon Form / A： |
| Complex Numbers / B： |
| Glossary |
| Answers to Odd-Numbered Exercises |
| Index |
| Linear Equations in Linear Algebra / 1： |
| Introductory Example: Linear Models in Economics and Engineering |
| Systems of Linear Equations / 1.1： |
図書
