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| Preface | |
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| Conventions and Notations | |
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| An Introduction To Maple� | |
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| The Commands | |
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| Programming | |
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| Linear Systems of Equations and Matrices | |
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| Linear Systems of Equations | |
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| Augmented Matrix of a Linear System and Row Operations | |
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| Some Matrix Arithmetic | |
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| Gauss-Jordan Elimination and Reduced Row Echelon Form | |
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| Gauss-Jordan Elimination and rref | |
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| Elementary Matrices | |
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| Sensitivity of Solutions to Error in the Linear System | |
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| Applications of Linear Systems and Matrices | |
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| Applications of Linear Systems to Geometry | |
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| Applications of Linear Systems to Curve Fitting | |
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| Applications of Linear Systems to Economics | |
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| Applications of Matrix Multiplication to Geometry | |
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| An Application of Matrix Multiplication to Economics | |
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| Determinants, Inverses, and Cramer's Rule | |
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| Determinants and Inverses from the Adjoint Formula | |
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| Determinants by Expanding Along Any Row or Column | |
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| Determinants Found by Triangularizing Matrices | |
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| LU Factorization | |
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| Inverses from rref | |
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| Cramer's Rule | |
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| Basic Linear Algebra Topics | |
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| Vectors | |
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| Dot Product | |
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| Cross Product | |
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| Vector Projection | |
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| A Few Advanced Linear Algebra Topics | |
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| Rotations in Space | |
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| "Rolling" a Circle Along a Curve | |
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| The TNB Frame | |
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| Independence, Basis, and Dimension for Subspaces of R<sup>n</sup> | |
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| Subspaces of R<sup>n</sup> | |
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| Independent and Dependent Sets of Vectors in R<sup>n</sup> | |
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| Basis and Dimension for Subspaces of R<sup>n</sup> | |
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| Vector Projection onto a Subspace of R<sup>n</sup> | |
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| The Gram-Schmidt Orthonormalization Process | |
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| Linear Maps from R<sup>n</sup> to R<sup>n</sup> | |
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| Basics About Linear Maps | |
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| The Kernel and Image Subspaces of a Linear Map | |
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| Composites of Two Linear Maps and Inverses | |
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| Change of Bases for the Matrix Representation of a Linear Map | |
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| The Geometry of Linear and Affine Maps | |
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| The Effect of a Linear Map on Area and Arclength in Two Dimensions | |
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| The Decomposition of Linear Maps into Rotations, Reflections, and Rescalings in R<sup>2</sup> | |
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| The Effect of Linear Maps on Volume, Area, and Arclength in R<sup>3</sup> | |
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| Rotations, Reflections, and Rescalings in Three Dimensions | |
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| Affine Maps | |
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| Least-Squares Fits and Pseudoinverses | |
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| Pseudoinverse to a Nonsquare Matrix and Almost Solving an Overdetermined Linear System | |
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| Fits and Pseudoinverses | |
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| Least-Squares Fits and Pseudoinverses | |
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| Eigenvalues and Eigenvectors | |
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| What Are Eigenvalues and Eigenvectors, and Why Do We Need Them? | |
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| Summary of Definitions and Methods for Computing Eigenvalues and Eigenvectors as well as the Exponential of a Matrix | |
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| Applications of the Diagonalizability of Square Matrices | |
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| Solving a Square First-Order Linear System of Differential Equations | |
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| Basic Facts About Eigenvalues, Eigenvectors, and Diagonalizability | |
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| The Geometry of the Ellipse Using Eigenvalues and Eigenvectors | |
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| A Maple Eigen-Procedure | |
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| Suggested Reading | |
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| Indices | |
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| Keyword Index | |
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| Index of Maple Commands and Packages | |