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Introductory Linear Algebra | |
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Linear Equations and Matrices | |
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Linear Systems | |
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Matrices | |
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Dot Product and Matrix Multiplication | |
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Properties of Matrix Operations | |
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Graph Theory (Optional) | |
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Solutions of Linear Systems of Equations | |
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Electrical Circuits (Optional) | |
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Markov Chains (Optional) | |
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The Inverse of a Matrix | |
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Linear Economic Models (Optional) | |
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Wavelets (Optional) | |
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LU-Factorization (Optional) | |
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Determinants | |
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Definition and Properties | |
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Cofactor Expansion and Applications | |
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Determinants from a Computational Point of View | |
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Vectors in R2 and R3 | |
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Vectors in the Plane | |
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N-Vectors | |
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Introduction to Linear Transformations | |
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Computer Graphics | |
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Computer Graphics (Optional) | |
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Cross Products in R3 (Optional) | |
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Lines and Planes | |
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Real Vector Spaces | |
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Real Vector Spaces | |
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Subspaces | |
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Linear Independence | |
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Basis and Dimension | |
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Homogeneous Systems | |
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The Rank of a Matrix and Applications | |
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Coordinates and Change of Basis | |
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Orthonormal Bases in Rn | |
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QR-Factorization (Optional) | |
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Orthogonal Complements | |
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Least Squares (Optional) | |
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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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Diagonalization and Symmetric Matrices | |
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Linear Transformations and Matrices | |
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Definition and Examples | |
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The Kernel and Range of a Linear Transformation | |
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The Matrix of a Linear Transformation | |
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Cumulative Review of Part I | |
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OTHER APPLICATIONS | |
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Linear Programming | |
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The Linear Programming Problem | |
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Geometric Solution | |
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The Simplex Method | |
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Duality | |
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The Theory of Games | |
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Applications of Eigenvalues and Eigenvectors | |
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The Fibonacci Sequence | |
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Differential Equations (Calculus Required) | |
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Dynamical Systems (Calculus Required) | |
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Intro to Fractals | |
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Quadratic Forms | |
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Conic Sections | |
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Quadric Surfaces | |
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Introduction to MATLAB | |
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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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Further Directions | |
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Inner Product Spaces (Calculus Required) | |
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Composite and Invertible Linear Transformations | |
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Answers to Odd-Numbered Exercises and Chapter Tests | |
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Index | |