The readings are assigned in: Strang, Gilbert. Introduction to Linear Algebra. 4th ed. Wellesley, MA: Wellesley-Cambridge Press, February 2009. ISBN: 9780980232714.  The Table of Contents is listed below.

1The geometry of linear equations1.1-2.1
2Elimination with matrices2.2-2.3
3Matrix operations and inverses2.4-2.5
4LU and LDU factorization2.6
5Transposes and permutations2.7
6Vector spaces and subspaces3.1
7The nullspace: Solving Ax = 03.2
8Rectangular PA = LU and Ax = b3.3-3.4
9Row reduced echelon form3.3-3.4
10Basis and dimension3.5
11The four fundamental subspaces3.6
12Exam 1: Chapters 1 to 3.4
13Graphs and networks8.2
14Orthogonality4.1
15Projections and subspaces4.2
16Least squares approximations4.3
17Gram-Schmidt and A = QR4.4
18Properties of determinants5.1
19Formulas for determinants5.2
20Applications of determinants5.3
21Eigenvalues and eigenvectors6.1
22Diagonalization6.2
23Markov matrices8.3
24Review for exam 2
25Exam 2: Chapters 1-5, 6.1-6.2, 8.2
26Differential equations6.3
27Symmetric matrices6.4
28Positive definite matrices6.5
29Matrices in engineering8.1
30Similar matrices6.6
31Singular value decomposition6.7
32Fourier series, FFT, complex matrices8.5, 10.2-10.3
33Linear transformations7.1-7.2
34Choice of basis7.3
35Linear programming8.4
36Course review
37Exam 3: Chapters 1-8 (8.1, 2, 3, 5)
38Numerical linear algebra9.1-9.3
39Computational scienceSee the Web site for 18.085
40Final exam

### 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 and Preconditioners

### 10. Complex Vectors and Complex Matrices

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