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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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| Matrix Transformations | |
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| Solutions of Linear Systems of Equations | |
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| The Inverse of a Matrix | |
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| LU-Factorization (Optional) | |
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| Applications of Linear Equations and Matrices (Optional) | |
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| An Introduction to Coding | |
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| Computer Graphics | |
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| Graph Theory | |
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| Electrical Circuits | |
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| Markov Chains | |
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| Linear Economic Models | |
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| Introduction to Wavelets | |
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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 inRn | |
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| Vectors in the Plane | |
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| n-Vectors | |
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| Linear Transformations | |
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| Applications of Vectors inR2andR3(Optional) | |
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| Cross Products inR3 | |
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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 inRn | |
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| Orthogonal Complements | |
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| Applications of Real Vector Spaces (Optional) | |
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| QR-Factorization | |
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| Least Square Lines | |
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| More on Coding | |
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| Eigenvalues, Eigenvectors, and Diagonalization | |
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| Eigenvalues and Eigenvectors | |
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| Diagonalization and Similar Matrices | |
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| Diagonalization of Symmetric Matrices | |
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| Applications of Eigenvalues and Eigenvectors (Optional) | |
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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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| Quadratic Forms | |
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| Conic Sections | |
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| Quadric Surfaces | |
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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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| Introduction to Fractals (Optional) | |
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| Cumulative Review of Introductory Linear Algebra | |
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| Linear Programming (Optional) | |
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| The Linear Programming Problem; 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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| 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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| 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 | |