# Book:Gilbert Strang/Introduction to Linear Algebra/Fourth Edition

## Gilbert Strang: Introduction to Linear Algebra (4th Edition)

Published $\text {2009}$

### Contents

Chapter 1: Matrices and Gaussian Elimination
1.1 Introduction
1.2 The Geometry of Linear Equations
1.3 An Example of Gaussian Elimination
1.4 Matrix Notation and Matrix Multiplication
1.5 Triangular Factors and Row Exchanges
1.6 Inverses and Transposes
1.7 Special Matrices and Applications
Review Exercises: Chapter 1
Chapter 2: Vector Spaces
2.1 Vector Spaces and Subspaces
2.2 Solving $A x = 0$ and $A x = b$
2.3 Linear Independence, Basis and Dimension
2.4 The Four Fundamental Subspaces
2.5 Graphs and Networks
2.6 Linear Transformations
Review Exercises: Chapter 2
Chapter 3: Orthogonality
3.1 Orthogonal Vectors and Subspaces
3.2 Cosines and Projections onto Lines
3.3 Projections and Least Squares
3.4 Orthogonal Bases and Gram-Schmidt
3.5 The Fast Fourier Transform
Review Exercises: Chapter 3
Chapter 4: Determinants
4.1 Introduction
4.2 Properties of the Determinant
4.3 Formulas for the Determinant
4.4 Applications of Determinants
Review Exercises: Chapter 4
Chapter 5: Eigenvalues and Eigenvectors
5.1 Introduction
5.2 Diagonalization of a Matrix
5.3 Difference Equations and Powers $A^k$
5.4 Differential Equations and $e^{A t}$
5.5 Complex Matrices
5.6 Similarity Transformations
Review Exercises: Chapter 5
Chapter 6: Positive Definite Matrices
6.1 Minima, Maxima, and Saddle Points
6.2 Tests for Positive Definiteness
6.3 Singular Value Decomposition
6.4 Minimum Principles
6.5 The Finite-Element Method
Chapter 7: Computations with Matrices
7.1 Introduction
7.2 Matrix Norm and Condition Number
7.3 Computation of Eigenvalues
7.4 Iterative Methods for $A x = b$
Chapter 8: Linear Programming and Game Theory
8.1 Linear Inequalities
8.2 The Simplex Method
8.3 The Dual Problem
8.4 Network Models
8.5 Game Theory
Appendix 1: Intersection, Sum and Product of Spaces
Appendix 2: The Jordan Form

Solutions to Selected Exercises
Matrix Factorizations
Glossary
MATLAB Teaching Codes
Index
Linear Algebra in a Nutshell