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

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