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### Linear Algebra and Its Applications (Fourth Edition) by Gilbert Strang

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• 1. MATRICES AND GAUSSIAN EL-1
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

• 2. VECTOR
2.1 Vector Spaces and Subspaces
2.2 Solving Ax = 0 and Ax = 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

• 3. TGALIY
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

• 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

• 5. EI E V L ES AND EEIGENVECTORS
5.1 Introduction 233
5.2 Diagonalization of a Matrix
5.3 Difference Equations and Powers Ak
5.4 Differential Equations and eAt
5.5 Complex Matrices 280
5.6 Similarity Transformations
Review Exercises: Chapter 5

• 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

• 7. COMPUTATIONS WITH MATRICES
7.1 Introduction
7.2 Matrix Number
7.3 Computation of Eigenvalues
7.4 Iterative Methods for Ax = b

• 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
INTERSECTION, SUM, AND PRODUCT OF SPACES
THE JORDAN FORM
Solutions to Selected Exercises
Matrix Factorizations
Glossary
MATLAB Teaching Codes
Index
Linear Algebra in a Nutshell

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