1 
The Geometry of Linear Equations 

2 
Elimination with Matrices 

3 
Matrix Operations and Inverses 

4 
LU and LDU Factorization 
Problem set 1 due 
5 
Transposes and Permutations 

6 
Vector Spaces and Subspaces 

7 
The Nullspace: Solving Ax = 0 
Problem set 2 due 
8 
Rectangular PA = LU and Ax = b 

9 
Row Reduced Echelon Form 

10 
Basis and Dimension 
Problem set 3 due 
11 
The Four Fundamental Subspaces 

12 
Exam 1: Chapters 1 to 3.5 

13 
Graphs and Networks 

14 
Orthogonality 

15 
Projections and Subspaces 

16 
Least Squares Approximations 
Problem set 4 due 
17 
GramSchmidt and A = QR 

18 
Properties of Determinants 

19 
Formulas for Determinants 
Problem set 5 due 
20 
Applications of Determinants 

21 
Eigenvalues and Eigenvectors 

22 
Exam Review 
Problem set 6 due 
23 
Exam 2: Chapters 15 

24 
Diagonalization 

25 
Markov Matrices 

26 
Fourier Series and Complex Matrices 

27 
Differential Equations 

28 
Symmetric Matrices 
Problem set 7 due 
29 
Positive Definite Matrices 

30 
Matrices in Engineering 
Problem set 8 due 
31 
Singular Value Decomposition 

32 
Similar Matrices 

33 
Linear Transformations 
Problem set 9 due 
34 
Choice of Basis 

35 
Exam Review 

36 
Exam 3: Chapters 18 (8.1, 2, 3, 5) 

37 
Fast Fourier Transform 

38 
Linear Programming 

39 
Numerical Linear Algebra 

40 
Final Exams 
