Readings

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

SES #TOPICSREADINGS
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 

Table of Contents

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