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Systems Of Linear Equations And Matrices | |
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Introduction to Systems of Linear Equations | |
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Gaussian Elimination | |
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Matrices and Matrix Operations | |
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Inverses Algebraic Properties of Matrices | |
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Elementary Matrices and a Method for Finding A-1 | |
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More on Linear Systems and Invertible Matrices | |
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Diagonal, Triangular, and Symmetric Matrices | |
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Applications of Linear Systems (Traffic flow Electrical Networks Balancing Chemical Equations, Polynomial Interpolation) | |
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Leontief Input-Output Models * Chapter Summary | |
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Determinants | |
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Determinants by Cofactor Expansion | |
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Evaluating Determinants by Row Reduction | |
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Properties of Determinants Adjoint Cramer's Rule * Chapter Summary | |
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Euclidean Vector Spaces | |
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Vectors in 2-space, 3-space, and n-space | |
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Norm, Dot Product, and Distance in Rn | |
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Orthogonality | |
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The Geometry of Linear Systems | |
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Cross Product * Chapter Summary | |
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General Vector Spaces | |
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Real Vector Spaces | |
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Subspaces | |
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Linear Independence | |
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Coordinates and Basis | |
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Dimension | |
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Change of Basis | |
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Row Space, Column Space, and Null Space | |
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Rank, Nullity, and the Fundamental Matrix Spaces | |
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Linear Transformations from Rn to Rm | |
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Properties of Matrix Transformations from Rn to Rm | |
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Geometry of Matrix Operators | |
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Dynamical Systems and Markov Chains * Chapter Summary | |
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Eignvalues And Eigenvectors | |
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Eigenvalues and Eigenvectors | |
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Diagonalization | |
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Complex Vector Spaces | |
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Application to Differential Equations * Chapter Summary | |
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Inner Product Spaces | |
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Inner Products | |
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Angle and Orthogonality in Inner Product Spaces | |
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Orthonormal Bases Gram-Schmidt Process QR - Decomposition | |
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Best Approximation Least Squares | |
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Least Squares Fitting to Data | |
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Fourier Series * Chapter Summary | |
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Diagonalization And Quadratic Forms | |
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Orthogonal Matrices | |
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Orthogonal Diagonalization | |
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Quadratic Forms | |
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Application of Quadratic Forms to Optimization | |
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Hermitian, Unitary, and Normal Matrices * Chapter Summary | |
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Linear Transformations | |
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General Linear Transformations | |
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Isomorphism | |
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Composition and Inverse Transformations | |
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Matrices of General Linear Transformations | |
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Similarity * Chapter Summary | |
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Numerical Methods | |
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Matrix Factorization and LU-Decompositions | |
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The Power Method | |
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Application to Internet Search Engines | |
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Comparison of Procedures for Solving Linear Systems | |
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Singular-Value Decomposition | |
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Application of Singular Value Decomposition to Data Compression * Chapter Summary | |