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

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

Published $\text {2009}$

Subject Matter

• Linear Algebra

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

Further Editions

• 1993: Gilbert Strang: Introduction to Linear Algebra
• 2016: Gilbert Strang: Introduction to Linear Algebra (5th ed.)