1. Linear Equations
1.1 Introduction to Linear Systems
1.2 Matrices, Vectors, and Gauss-Jordan Elimination
1.3 On the Solutions of Linear Systems; Matrix Algebra
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2. Linear Transformations
2.1 Introduction to Linear Transformations and Their Inverses
2.2 Linear Transformations in Geometry
2.3 Matrix Products
2.4 The Inverse of a Linear Transformation
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3. Subspaces of Rn and Their Dimensions
3.1 Image and Kernel of a Linear Transformation
3.2 Subspace of Rn; Bases and Linear Independence
3.3 The Dimension of a Subspace of Rn
3.4 Coordinates
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4. Linear Spaces
4.1 Introduction to Linear Spaces
4.2 Linear Transformations and Isomorphisms
4.3 The Matrix of a Linear Transformation
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5. Orthogonality and Least Squares
5.1 Orthogonal Projections and Orthonormal Bases
5.2 Gram-Schmidt Process and QR Factorization
5.3 Orthogonal Transformations and Orthogonal Matrices
5.4 Least Squares and Data Fitting
5.5 Inner Product Spaces
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6. Determinants
6.1 Introduction to Determinants
6.2 Properties of the Determinant
6.3 Geometrical Interpretations of the Determinant; Cramer's Rule
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7. Eigenvalues and Eigenvectors
7.1 Diagonalization
7.2 Finding the Eigenvalues of a Matrix
7.3 Finding the Eigenvectors of a Matrix
7.4 More on Dynamical Systems
7.5 Complex Eigenvalues
7.6 Stability
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8. Symmetric Matrices and Quadratic Forms
8.1 Symmetric Matrices
8.2 Quadratic Forms
8.3 Singular Values
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9. Linear Differential Equations
9.1 An Introduction to Continuous Dynamical Systems
9.2 The Complex Case: Euler's Formula
9.3 Linear Differential Operators and Linear Differential Equations
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Appendix A. Vectors
Appendix B: Techniques of Proof
Answers to Odd-numbered Exercises
Subject Index
Name Index