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| Note: All relevant chapters end with Supplementary Exercises. | |
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| Linear Equations and Matrices | |
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| Systems of Linear Equations | |
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| Matrices | |
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| Matrix Multiplication | |
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| Algebraic Properties of Matrix Operations | |
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| Special Types of Matrices and Partitioned Matrices | |
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| Matrix Transformations | |
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| Computer Graphics | |
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| Correlation Coefficient (Optional) | |
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| Solving Linear Systems | |
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| Echelon Form of a Matrix | |
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| Elementary Matrices: Finding A-1 | |
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| Equivalent Matrices | |
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| LU-Factorization (Optional) | |
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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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| Inner Product Spaces | |
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| Standard Inner Product on R2 and R3 | |
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| Cross Product in R3 (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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| 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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| Inroduction to Homogeneous Coordinates (Optional) | |
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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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| 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 | |
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| 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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| Dominant Eigenvalue and Principal Component Analysis (Optional) | |
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| Differential Equations (Optional) | |
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| Differential Equations | |
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| Dynamical Systems | |
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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 Sets Functions | |
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| Complex Numbers Complex Numbers Complex Numbers in Linear Algebra | |
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| Introduction to Proofs | |
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| Answers to Odd-Numbered Exercises | |
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| Index | |