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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:
Feb.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:
Feb.29Mar.4 
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:
Mar.711 
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:
Mar.1418 
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:
Mar.2125 
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:
Mar.28Apr.1 
15 
§8.3: Properties of Linear Transformations. 
16 
§8.4: Images and Kernels of Linear Transformations. 

17 
§8.5: Some Fundamental Constructions. 

Week 7:
Apr.48 
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:
Apr.1115 
21 
§10.2: Some Numerical Examples. 
22 
§10.3: Matrices and Their Algebra. 

23 
§10.4: Special Types of Matrices. 

Week 9:
Apr.1822 
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:
Apr.2529 
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:
May 26 
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:
May 913 
33 
§14.3: Determinants. 
34 
§14.4: The Characteristic Polynomial. 

35 
§14.5: Diagonalization Theorems. 

Week 13:
May 1620 
36 
§17.3: Jordan Form (parts of). 
37 
Chapter 15. Inner Product Spaces §15.1: Scalar Products. 

38 
§15.2: Inner Product Spaces. 

Holiday: Thursday, May 19  
Week 14:
May 2327 
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. 

FINAL EXAMS May 30  June 11 