Systems of Linear Equations
Chapter 1 Linear Equations in Linear Algebra
1-1 Systems of Linear Equations
1-2 Row Reduction and Echelon Forms
1-3 Vector Equations
1-4 The Matrix Equation Ax = b
1-5 Solution Sets of Linear Systems
1-6 Applications of Linear Systems
1-7 Linear Independence
1-8 Introduction to Linear Transformations
1-9 The Matrix of a Linear Transformation
Chapter 2 Matrix Algebra
2-1 Matrix Operations
2-2 The Inverse of a Matrix
2-3 Characterizations of Invertible Matrices
2-4 Partitioned Matrices
2-5 Matrix Factorizations
2-6 The Leontief Input-Output Model
2-7 Applications to Computer Graphics
Chapter 3 Determinants
3-1 Introduction to Determinants 172
3-2 Properties of Determinants 179
3-3 Cramer's Rule, Volume, and Linear Transformations
Chapter 4 Vector Spaces
4-1 Vector Spaces and Subspaces
4-2 Null Spaces, Column Spaces, Row Spaces, and Linear Transformations
4-3 Linearly Independent Sets; Bases
4-4
4-5 The Dimension of a vector space
4-6 Change of Basis
4-7 Digital Signal Processing
4-8 Applications to Difference Equations
Chapter 5 Eigenvalues and Eigenvectors
5-1 Eigenvalues and Eigenvectors
5-2 The Characteristic Equation
5-3 Diaganolization
5-4 Eigenvectors. And Linear Transformation
5-5 Complex Eigenvalues
5-6 Discrete Dynamical Systems
Chapter 6 Orthogonality and Least Squares
6.1 Inner Product, Length, and Orthogonality
6.2 Orthogonal Sets
6.3 Orthogonal Projections
6.4 The Gram-Schmidt Process
6.5 Least-Squares Problems
6.7 Inner Product Spaces
6.8 Applications of Inner product Spaces
Chapter 7
7.1 Diagonalization of Symmetric Matrices
7.2 Quadratic Forms
7.3 Constrained Optimization
7.4 The Singular Value Decomposition
7.5 Applications to Image Processing and Statistics
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