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Students should use
ODTUClass
There will be a total of 42 one hour units in the course. Each week, three units will be taught.
The contents of each unit are listed below, where the section numbers refer to the course textbook by L. Smith.
Note: This schedule may be modified/reorganized as the class progresses.
Week 0:
Feb.1415 
0  Introduction to the Course 
Week 1:
Feb.1822 
1 
Chapter 2. Vector Spaces §2.1: Axioms for Vector Spaces. 
2 
§2.2: Cartesian (or Euclidean) Spaces. §2.3: Some Rules for Vector Algebra. 

3 
Chapter 3. Examples of Vector Spaces §3.1: Three Basic Examples. 

Week 2:
Feb.25Mar.1 
4 
§3.2: Further Examples of Vector Spaces. 
5 
Chapter 4. Subspaces §4.1: Basic Properties of Vector Subspaces. 

6 
§4.2: Examples of Subspaces. 

Week 3:
Mar.48 
7 
Chapter 5. Linear Independence and Dependence §5.1: Basic Definitions and Examples. 
8 
§5.2: Properties of Independent and Dependent Sets. 

9 
Chapter 6. FiniteDimensional Vector Spaces and Bases §6.1: FiniteDimensional Vector Spaces. 

Week 4:
Mar.1115 
10 
§6.2: Properties of Bases. 
11 
§6.3: Using Bases. 

12 
Chapter 7. The Elements of Vector Spaces: A Summing Up §7.1: Numerical Examples. 

Week 5:
Mar.1822 
13 
Chapter 8. Linear Transformations §8.1: Definition of Linear Transformations. 
MIDTERM 1: Wednesday, 20 March at 17:40 Rooms SZ22, SZ23 

14 
§8.2: Examples of Linear Transformations. 

15 
§8.3: Properties of Linear Transformations. 

Week 6:
Mar.2529 
16 
§8.4: Images and Kernels of Linear Transformations. 
17 
§8.5: Some Fundamental Constructions. 

18 
§8.6: Isomorphism of Vector Spaces. 

Week 7:
Apr.15 
19 
Chapter 9. Linear Transformations: Examples and Applications §9.1: Numerical Examples. 
20 
Chapter 10. Linear Transformations and Matrices §10.1: Linear Transformations and Matrices in R^{2}. 

21 
§10.2: Some Numerical Examples. 

Week 8:
Apr.813 
22 
§10.3: Matrices and Their Algebra. 
23 
§10.4: Special Types of Matrices. 

24 
Chapter 11. Representing Linear Transformations by Matrices §11.1: Representing a Linear Transformation by a Matrix. 

Week 9:
Apr.1519 
25 
§11.2: Basic Theorems. 
26 
§11.3: Change of Bases. 

27 
Chapter 12. More on Representing Linear Transformations by Matrices §12.1: Projections. §12.2: Nilpotent Transformations. §12.3: Cyclic Transformations. 

Week 10:
Apr.2226 
28 
Chapter 13. Systems of Linear Equations §13.1: Existence Theorems. 
Holiday April 23 MIDTERM 2: Wednesday, 24 April at 17:40 

29 
§13.2: Reduction to Echelon Form. 

Week 11:
Apr.29May 3 
30 
§13.2: Reduction to Echelon Form (cont). 
Holiday May 1  
31 
Chapter 14. The Elements of Eigenvalue and Eigenvector Theory §14.1: The Rank of an Endomorphism. 

Week 12:
May 610 
32 
§14.2: Eigenvalues and Eigenvectors. 
33 
§14.3: Determinants. 

34 
§14.4: The Characteristic Polynomial. 

Week 13:
May 1317 
35 
§14.5: Diagonalization Theorems. 
36 
§17.3: Jordan Form (parts of). 

37 
Chapter 15. Inner Product Spaces §15.1: Scalar Products. 

Week 14:
May 2024 
38 
§15.2: Inner Product Spaces. 
39 
§15.3: Isometries. 

40 
Additional Topics and Applications §15.4: The Riesz Representation Theorem. 

FINAL EXAM: Friday, 7 June at 9:00 