Linear Algebra: A Modern Introduction – David Poole – 4th Edition

1 Vectors
1.1 The Geometry and Algebra of Vectors
1.2 Length and Angle: The Dot Product
Exploration: Vectors and Geometry
1.3 Lines and Planes
Exploration: The Cross Product
1.4 Applications
Chapter Review

2 Systems of Linear Equations
2.1 Introduction to Systems of Linear Equations
2.2 Direct Methods for Solving Linear Systems
Exploration: Lies My Computer Told Me
Exploration: Partial Pivoting
Exploration: An Introduction to the Analysis of Algorithms
2.3 Spanning Sets and Linear Independence
2.4 Applications
2.5 Iterative Methods for Solving Linear Systems
Chapter Review

3 Matrices
3.1 Matrix Operations
3.2 Matrix Algebra
3.3 The Inverse of a Matrix
3.4 The LU Factorization
3.5 Subspaces, Basis, Dimension, and Rank
3.6 Introduction to Linear Transformations
3.7 Applications
Chapter Review

4 Eigenvalues and Eigenvectors
4.1 Introduction to Eigenvalues and Eigenvectors
4.2 Determinants
Exploration: Geometric Applications of Determinants
4.3 Eigenvalues and Eigenvectors of n × n Matrices
4.4 Similarity and Diagonalization
4.5 Iterative Methods for Computing Eigenvalues
4.6 Applications and the Perron-Frobenius Theorem
Chapter Review

5 Orthogonality
5.1 Orthogonality in Rn
5.2 Orthogonal Complements and Orthogonal Projections
5.3 The Gram-Schmidt Process and the QR Factorization
Exploration: The Modified QR Process
Exploration: Approximating Eigenvalues with the QR Algorithm
5.4 Orthogonal Diagonalization of Symmetric Matrices
5.5 Applications
Chapter Review

6 Vector Spaces
6.1 Vector Spaces and Subspaces
6.2 Linear Independence, Basis, and Dimension
Exploration: Magic Squares
6.3 Change of Basis
6.4 Linear Transformations
6.5 The Kernel and Range of a Linear Transformation
6.6 The Matrix of a Linear Transformation
Exploration: Tiles, Lattices, and the Crystallographic Restriction
6.7 Applications
Chapter Review

7 Distance and Approximation
7.1 Inner Product Spaces
Exploration: Vectors and Matrices with Complex Entries
Exploration: Geometric Inequalities and Optimization Problems
7.2 Norms and Distance Functions
7.3 Least Squares Approximation
7.4 The Singular Value Decomposition
7.5 Applications
Chapter Review

8 Codes
8.1 Code Vectors
8.2 Error-Correcting Codes
8.3 Dual Codes
8.4 Linear Codes
8.5 The Minimum Distance of a Code