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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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MATLAB 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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Partitioned Matrices and Block Multiplication | |
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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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MATLAB 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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MATLAB 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 Dimension 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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MATLAB 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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MATLAB Exercises | |
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Orthogonality | |
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The Geometry of Vectors | |
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Orthogonal Vectors | |
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Orthogonal Projections | |
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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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Principal Component Analysis | |
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Rotations of R[superscript 3] and Computer Graphics | |
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Review Exercises | |
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MATLAB Exercises | |
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Vector Spaces | |
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Vector Spaces and Their Subspaces | |
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Linear Transformations | |
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Basis and Dimension | |
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Matrix Representations of Linear Operators | |
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Inner Product Spaces | |
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Review Exercises | |
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MATLAB Exercises | |
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Appendices | |
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Sets | |
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Functions | |
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Complex Numbers | |
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MATLAB | |
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The Uniqueness of the Reduced Row Echelon Form | |
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Bibliography | |
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Answers to Selected Exercises | |
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Index | |