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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 | |