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| Preface | |
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| To the Student | |
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| Matrices, Vectors, and Systems of Linear Equations | |
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| Matrices and Vectors | |
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| Linear Combinations, Matrix-Vector Products, and Special Matrices | |
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| Systems of Linear Equations | |
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| Gaussian Elimination | |
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| Applications of Systems of Linear Equations | |
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| The Span of a Set of Vectors | |
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| Linear Dependence and Linear Independence | |
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| Review Exercises | |
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| Matrices and Linear Transformations | |
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| Matrix Multiplication | |
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| Applications of Matrix Multiplication | |
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| Invertibility and Elementary Matrices | |
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| The Inverse of a Matrix | |
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| The LU Decomposition of a Matrix | |
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| Linear Transformations and Matrices | |
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| Composition and Invertibility of Linear Transformations | |
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| Review Exercises | |
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| Determinants | |
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| Cofactor Expansion | |
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| Properties of Determinants | |
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| Review Exercises | |
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| Subspaces and Their Properties | |
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| Subspaces | |
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| Basis and Dimension | |
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| The Dimensions of Subspaces Associated with a Matrix | |
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| Coordinate Systems | |
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| Matrix Representations of Linear Operators | |
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| Review Exercises | |
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| Eigenvalues, Eigenvectors, and Diagonalization | |
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| Eigenvalues and Eigenvectors | |
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| The Characteristic Polynomial | |
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| Diagonalization of Matrices | |
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| Diagonalization of Linear Operators | |
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| Applications of Eigenvalues | |
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| Review Exercises | |
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| Orthogonality | |
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| The Geometry of Vectors | |
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| Orthogonal Vectors | |
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| Least-Squares Approximation and Orthogonal Projection Matrices | |
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| Orthogonal Matrices and Operators | |
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| Symmetric Matrices | |
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| Singular Value Decomposition | |
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| Rotations of R[superscript 3] and Computer Graphics | |
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| Review Exercises | |
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| Vector Spaces | |
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| Vector Spaces and Their Subspaces | |
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| Dimension and Isomorphism | |
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| Linear Transformations and Matrix Representations | |
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| Inner Product Spaces | |
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| Review Exercises | |
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| Complex Numbers | |
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| References | |
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| Answers to Odd-Numbered Exercises | |
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| Index | |