# Introduction to Linear Algebra, 4th Edition

## Publication early 2009Gilbert Strang      gs@math.mit.edu

### Wellesley-Cambridge Press and SIAM      (for ordering information)

#### Related websites:   web.mit.edu/18.06 , ocw.mit.edu

ISBN: , International Edition:
[ILA Table of Contents]

I hope this website will become a valuable resource for everyone learning and doing linear algebra. Here are key links:

** Each section in the Table of Contents links to problem sets, solutions,
** other websites, and all material related to the topic of that section.
** Readers are invited to propose possible links (write to gs@math.mit.edu)

#### Table of Contents for ILA

1   Introduction to Vectors

1.1 Vectors and Linear Combinations
1.2 Lengths and Dot Products
1.3 Matrices

2 Solving Linear Equations

2.1 Vectors and Linear Equations
2.2 The Idea of Elimination
2.3 Elimination Using Matrices
2.4 Rules for Matrix Operations
2.5 Inverse Matrices
2.6 Elimination = Factorization: A = LU
2.7 Transposes and Permutations

3 Vector Spaces and Subspaces

3.1 Spaces of Vectors
3.2 The Nullspace of A: Solving Ax = 0
3.3 The Rank and the Row Reduced Form
3.4 The Complete Solution to Ax = b
3.5 Independence, Basis and Dimension
3.6 Dimensions of the Four Subspaces

4 Orthogonality

4.1 Orthogonality of the Four Subspaces
4.2 Projections
4.3 Least Squares Approximations
4.4 Orthogonal Bases and Gram-Schmidt

5 Determinants

5.1 The Properties of Determinants
5.2 Permutations and Cofactors
5.3 Cramer's Rule, Inverses, and Volumes

6 Eigenvalues and Eigenvectors

6.1 Introduction to Eigenvalues
6.2 Diagonalizing a Matrix
6.3 Applications to Differential Equations
6.4 Symmetric Matrices
6.5 Positive Definite Matrices
6.6 Similar Matrices
6.7 Singular Value Decomposition (SVD)

7 Linear Transformations

7.1 The Idea of a Linear Transformation
7.2 The Matrix of a Linear Transformation
7.3 Diagonalization and the Pseudoinverse

8 Applications

8.1 Matrices in Engineering
8.2 Graphs and Networks
8.3 Markov Matrices, Population, and Economics
8.4 Linear Programming
8.5 Fourier Series: Linear Algebra for Functions
8.6 Linear Algebra for Statistics and Probability
8.7 Computer Graphics

9 Numerical Linear Algebra

9.1 Gaussian Elimination in Practice
9.2 Norms and Condition Numbers
9.3 Iterative Methods for Linear Algebra

10 Complex Vectors and Matrices

10.1 Complex Numbers
10.2 Hermitian and Unitary Matrices
10.3 The Fast Fourier Transform

Solutions to Selected Exercises
Matrix Factorizations
Conceptual Questions for Review
Glossary: A Dictionary for Linear Algebra
Index
Teaching Codes

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Each section of the book has a Problem Set.

The text also provides MATLAB codes to implement the key algorithms.

This page has been accessed at least times since January 2009. Last updated 01/07/2009.