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Preface | |
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Linear Equations and Matrices | |
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Systems of Linear Equations | |
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Matrices; Matrix Operations | |
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Algebraic Properties of Matrix Operations | |
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Special Types of Matrices and Partitioned Matrices | |
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Echelon Form of a Matrix | |
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Elementary Matrices; Finding A[superscript -1] | |
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Equivalent Matrices | |
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LU-Factorization (Optional) | |
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Supplementary Exercises | |
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Real Vector Spaces | |
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Vectors in the Plane and in 3-Space | |
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Vector Spaces | |
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Subspaces | |
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Span and Linear Independence | |
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Basis and Dimension | |
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Homogeneous Systems | |
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Coordinates and Isomorphisms | |
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Rank of a Matrix | |
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Supplementary Exercises | |
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Inner Product Spaces | |
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Standard Inner Product on R[superscript 2] and R[superscript 3] | |
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Cross Product in R[superscript 3] (Optional) | |
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Inner Product Spaces | |
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Gram-Schmidt Process | |
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Orthogonal Complements | |
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Least Squares (Optional) | |
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Supplementary Exercises | |
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Linear Transformations and Matrices | |
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Definition and Examples | |
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Kernel and Range of a Linear Transformation | |
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Matrix of a Linear Transformation | |
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Vector Space of Matrices and Vector Space of Linear Transformations (Optional) | |
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Similarity | |
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Computer Graphics (Optional) | |
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Supplementary Exercises | |
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Determinants | |
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Definition | |
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Properties of Determinants | |
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Cofactor Expansion | |
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Inverse of a Matrix | |
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Other Applications of Determinants | |
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Determinants from a Computational Point of View | |
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Supplementary Exercises | |
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Eigenvalues and Eigenvectors | |
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Eigenvalues and Eigenvectors | |
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Diagonalization and Similar Matrices | |
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Stable Age Distribution in a Population; Markov Processes (Optional) | |
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Diagonalization of Symmetric Matrices | |
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Spectral Decomposition and Singular Value Decomposition (Optional) | |
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Real Quadratic Forms | |
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Conic Sections | |
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Quadric Surfaces | |
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Supplementary Exercises | |
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Differential Equations (Optional) | |
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Differential Equations | |
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Dynamical Systems | |
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Supplementary Exercises | |
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Matlab for Linear Algebra | |
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Input and Output in MATLAB | |
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Matrix Operations in MATLAB | |
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Matrix Powers and Some Special Matrices | |
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Elementary Row Operations in MATLAB | |
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Matrix Inverses in MATLAB | |
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Vectors in MATLAB | |
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Applications of Linear Combinations in MATLAB | |
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Linear Transformations in MATLAB | |
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MATLAB Command Summary | |
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MATLAB Exercises | |
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Preliminaries | |
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Sets | |
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Functions | |
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Complex Numbers | |
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Complex Numbers | |
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Complex Numbers in Linear Algebra | |
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Answers to Odd-Numbered Exercises | |
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Index | |