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| (Each chapter begins with an Introductory Example and ends with Supplementary Exercises.) | |
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| Linear Equations In Linear Algebra | |
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| Introductory Example: Linear Models in Economics and Engineering | |
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| Systems of Linear Equations | |
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| Row Reduction and Echelon Forms | |
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| Vector Equations | |
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| The Matrix Equation Ax = b | |
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| Solution Sets of Linear Systems | |
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| Linear Independence | |
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| Introduction to Linear Transformations | |
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| The Matrix of a Linear Transformation | |
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| Linear Models in Business, Science, and Engineering | |
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| Supplementary Exercises | |
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| Matrix Algebra | |
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| Introductory Example: Computer Graphics in Automotive Design | |
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| Matrix Operations | |
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| The Inverse of a Matrix | |
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| Characterizations of Invertible Matrices | |
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| Partitioned Matrices | |
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| Matrix Factorizations | |
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| Iterative Solutions of Linear Systems | |
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| The Leontief Input-Output Model | |
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| Applications to Computer Graphics | |
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| Subspaces of Rn | |
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| Supplementary Exercises | |
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| Determinants | |
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| Introductory Example: Determinants in Analytic Geometry | |
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| Introduction to Determinants | |
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| Properties of Determinants | |
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| Cramer?s Rule, Volume, and Linear Transformations | |
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| Supplementary Exercises | |
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| Vector Spaces | |
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| Introductory Example: Space Flight and Control Systems | |
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| Vector Spaces and Subspaces | |
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| Null Spaces, Column Spaces, and Linear Transformations | |
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| Linearly Independent Sets; Bases | |
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| Coordinate Systems | |
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| The Dimension of a Vector Space | |
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| Rank | |
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| Change of Basis | |
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| Applications to Difference Equations | |
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| Applications to Markov Chains | |
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| Supplementary Exercises | |
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| Eigenvalues and Eigenvectors | |
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| Introductory Example: Dynamical Systems and Spotted Owls | |
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| Eigenvectors and Eigenvalues | |
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| The Characteristic Equation | |
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| Diagonalization | |
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| Eigenvectors and Linear Transformations | |
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| Complex Eigenvalues | |
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| Discrete Dynamical Systems | |
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| Applications to Differential Equations | |
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| Iterative Estimates for Eigenvalues | |
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| Supplementary Exercises | |
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| Orthogonality and Least-Squares | |
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| Introductory Example: Readjusting the North American Datum | |
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| Inner Product, Length, and Orthogonality | |
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| Orthogonal Sets | |
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| Orthogonal Projections | |
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| The Gram-Schmidt Process | |
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| Least-Squares Problems | |
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| Applications to Linear Models | |
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| Inner Product Spaces | |
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| Applications of Inner Product Spaces | |
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| Supplementary Exercises | |
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| Symmetric Matrices and Quadratic Forms | |
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| Introductory Example: Multichannel Image Processing | |
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| Diagonalization of Symmetric Matrices | |
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| Quadratic Forms | |
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| Constrained Optimization | |
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| The Singular Value Decomposition | |
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| Applications to Image Processing and Statistics | |
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| Supplementary Exercises | |
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| Appendices | |
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| Uniqueness of the Reduced Echelon Form | |
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| Complex Numbers | |
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| Glossary | |
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| Answers to Odd-Numbered Exercises | |
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| Index | |