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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 1:
Sept.2226 
0  Introduction to the Course 
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. 

Week 2:
Sept.29Oct.3 
3 
Chapter 3. Examples of Vector Spaces §3.1: Three Basic Examples. 
4 
§3.2: Further Examples of Vector Spaces. 

5 
Chapter 4. Subspaces §4.1: Basic Properties of Vector Subspaces. 

Week 3:
Oct.610 
6 
§4.2: Examples of Subspaces. 
7 
Chapter 5. Linear Independence and Dependence §5.1: Basic Definitions and Examples. 

8 
§5.2: Properties of Independent and Dependent Sets. 

Week 4:
Oct.1317 
9 
Chapter 6. FiniteDimensional Vector Spaces and Bases §6.1: FiniteDimensional Vector Spaces. 
10 
§6.2: Properties of Bases. 

11 
§6.3: Using Bases. 

Week 5:
Oct.2024 
12 
Chapter 7. The Elements of Vector Spaces: A Summing Up §7.1: Numerical Examples. 
13 
Chapter 8. Linear Transformations §8.1: Definition of Linear Transformations. 

14 
§8.2: Examples of Linear Transformations. 

Week 6:
Oct.2731 
15 
§8.3: Properties of Linear Transformations. 
Holiday: Wed., Oct. 29  
16 
§8.4: Images and Kernels of Linear Transformations. 

17 
§8.5: Some Fundamental Constructions. 

Week 7:
Nov.37 
18 
§8.6: Isomorphism of Vector Spaces. 
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}. 

Week 8:
Nov.1014 
21 
§10.2: Some Numerical Examples. 
22 
§10.3: Matrices and Their Algebra. 

23 
§10.4: Special Types of Matrices. 

Week 9:
Nov.1721 
24 
Chapter 11. Representing Linear Transformations by Matrices §11.1: Representing a Linear Transformation by a Matrix. 
25 
§11.2: Basic Theorems. 

26 
§11.3: Change of Bases. 

Week 10:
Nov.2428 
27 
Chapter 12. More on Representing Linear Transformations by Matrices §12.1: Projections. §12.2: Nilpotent Transformations. §12.3: Cyclic Transformations. 
28 
Chapter 13. Systems of Linear Equations §13.1: Existence Theorems. 

29 
§13.2: Reduction to Echelon Form. 

Week 11:
Dec.15 
30 
§13.2: Reduction to Echelon Form (cont). 
31 
Chapter 14. The Elements of Eigenvalue and Eigenvector Theory §14.1: The Rank of an Endomorphism. 

32 
§14.2: Eigenvalues and Eigenvectors. 

Week 12:
Dec.812 
33 
§14.3: Determinants. 
34 
§14.4: The Characteristic Polynomial. 

35 
§14.5: Diagonalization Theorems. 

Week 13:
Dec.1519 
36 
§17.3: Jordan Form (parts of). 
37 
Chapter 15. Inner Product Spaces §15.1: Scalar Products. 

38 
§15.2: Inner Product Spaces. 

Week 14:
Dec.2026 
39 
§15.3: Isometries. 
40 
Additional Topics and Applications §15.4: The Riesz Representation Theorem. 

41 
Chapter 16. The Spectral Theorem and Quadratic Forms §16.1: SelfAdjoint Transformations. 

Week 15:
Dec.2930 
42 
§16.2: The Spectral Theorem. 
FINAL EXAM 