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Table of Contents
Chapter 1: Matrices and Systems of Equations
Section 1.1: Systems of Linear Equations
Section 1.2: Row Echelon Form
Section 1.3: Matrix Algebra
Section 1.4 Elementary Matrices
Section 1.5: Partitioned Matrices
Chapter 2: Determinants
Section 2.1: The Determinant of a Matrix
Section 2.2: Properties of Determinants
Section 2.3: Cramer's Rule
Chapter 3: Vector Spaces
Section 3.1 Definition and Examples
Section 3.2: Subspaces
Section 3.3: Linear Independence
Section 3.4: Basis and Dimension
Section 3.5: Change of Basis
Section 3.6: Row Space and Column Space
Chapter 4: Linear Transformations
Section 4.1: Linear Transformations: Def
Section 4.2: Matrix Representations of L
Section 4.3: Similarity
Chapter 5: Orthogonality
Section 5.1: The Scalar Product in R
Section 5.2: Orthagonal Subspaces
Section 5.3: Least Squares Problems
Section 5.4: Inner Product Spaces
Section 5.5: Orthonormal Sets
Section 5.6: The Gram-Schmidt Orthogonal
Section 5.7: Orthogonal Polynomials
Chapter 6: Eigenvalues
Section 6.1: Eigenvalues and Eigenvector
Section 6.2: Systems of Linear Different
Section 6.3: Diagonalization
Section 6.4: Hermitian Matrices
Section 6.5: The Singular Value Decomposition
Section 6.6: Quadratic Forms
Section 6.7: Positive Definite Matrices
Section 6.8: Nonnegative Matrices
Chapter 7: Numerical Linear Algebra
Chapter 1: Section 7.1: Floating-Point Numbers
Chapter 2: Section 7.2: Gaussian Elimination
Chapter 3: Section 7.3: Pivoting Strategies
Chapter 4: Section 7.4: Matrix Norms and Condition Numbers
Chapter 5: Section 7.5: Orthogonal Transformations
Chapter 6: Section 7.6: The Eigenvalue Problem
Chapter 7: Section 7.7: Least Squares Problems
Chapter 8: Iterative Methods
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Chapter 9: Canonical Forms
Author's Website
ATLAST Project
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