Math 309: Intermediate Linear Algebra, Spring 2020

Instructor: Chi-Kwong Li

Meeting time and place: TT 9:30 - 10:50 a.m. Jones 301
Office: Jones 128, Tel: 221-2042
E-mail: ckli@math.wm.edu, http://cklixx.people.wm.edu
Office hours: TWR 11:00 a.m. - 12:30 a.m. or by appointments.

Course description: We will study linear algebra techniques in applied topics including such as large matrix computation, image processing, compressed sensing, optimization, neural nets, stochastic gradient descent and backpropagation.

Textbook: Gilbert Strang, Linear Algebra and Learning from Data, Wellesley Cambridge Press.

We will cover Part I, II, III, and selected material from Part IV - VII.
Here is a picture of the author and me taken at the 2020 AMS-MAA joint meeting, on Jan.17, at Denver.

Some useful references

• R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press.
• G. Strang, Linear Algebra and its Applications, Thompson Brooks/Cole.
• F. Zhang, Matrix theory: Basic results and techniques, Springer.

Homework will be assigned every lecture and due the following Friday (noon).
Homework help sessions will be conducted on Thursday, 11:00-noon Jones 113 or 131. Of course, help is also available at other office hours and by appointment.

Challenging problems will be assigned from time to time;
extra-credits will be given to successful (or partially successful) attempts.
You have to use LaTex to typset mathematical document.

LaTex

• You may use the online editor Write LaTeX .
• Here is a list of TeX commands for mathematics symbols.
• You may also download the Tex Program to your computer.
• Sample files for typesetting matrices and symbols used in this class. pdf file. LaTex file.
• Exercises I.1 - I.7.

            
     Exams:  Mid-term 1  Feb.  27  1:20 hrs  (9:30-11:50)
             Mid-term 2  April 2   1:20 hrs  (9:30-11:50)
             Final       May  13    3    hrs  (9:00-noon)
    
     Grades (for homework, exams, final grade, etc.):

     %: 0 - 60 - 65 - 70 - 75 - 80 - 83 - 87 - 90 - 93 - 100
          F    D    C-   C    C+   B-   B    B+   A-    A
     
     Assessment: Homework   Mid-term I   Mid-term II    Final  
    
                   25%        20%           20%          35%
   
               (Extra credit problems may add up to another 5%)

     One may choose to do a project for 15% (subject to approval) 
     so that the Final will weight 20% for the final assessment.

Exam 1 and sample soluton.

Exam 2 with sample solution. [ Tex file.]

Final examination paper. [Tex file.]

Class notes (Under continuous revision)

• Notes on I.1-I.9.
  [ Scanned note on Lecutre on Jan 23, 2020. ] [ Scanned note on Lecutre on Jan 28, 2020. ]
  [ Scanned note on Lecutre on Jan 30, 2020. ] [ Scanned note on Lecutre on Feb. 4, 2020. ]
  [ Scanned note on Lecutre on Feb. 6, 2020. ] [ Scanned note on Lecutre on Feb. 11, 2020. ]
  [ Scanned note on Lecutre on Feb. 13, 2020. ] [ Scanned note on Lecutre on Feb. 18, 2020. ]
  [ Scanned note on Lecutre on Feb. 20, 2020. ] [ Scanned note on Lecutre on Feb. 25, 2020. ]
  [ Lecture on March 3, 2020. See printed class note pp. 20-21.] [ Scanned note on Lecutre on March 5, 2020. ]
  
• Notes on I.9 - I-12 and after used in the Zoom meetings.
• Notes on Secton III.

• Homework 1. (Due: noon. Jan. 31, 2020).
  Problem Set I.1, #2, 6, 9, 10/11, 14. [ Sample solution. ]
• Homework 2. (Due: noon. Feb. 7)
  Problem I.2 #7, I.3 #4, 7 (Explain your answer), 10, I.4, # 3 (Use the tehnique in #4), 5, 6, 7, 10, 11. [ Sample solution. ]
• Homework 3. (Due: noon. Feb. 14)
  I.5 # 1, 4, 5, 6, 7. I.6 # 1, 4, 6, 12, 15, 23. [ Sample solution. ]
• Homework 4. (Due: noon. Feb. 21)
  I.6. #25. I.7 # 1, 2, 3, 4, 5, 6, 7, 8, 9. [ Sample solution. ]
• Homework 5. (Due: 2:00 p.m. Feb. 28)
  I.7. # 12, 14, (Hint: S is of rank one and of the form vv^t), 15, 16, 22, 26, 28. [ Sample solution. ]
• Homework 6. (Due 2:00 p.m. March 6)
  I.8. #2, 3, 4, 5, 7, 15, 17 (with explanation), 20, 21. [ Sample solution. ]
• Homework 7. (Due 2:00 p.m. March 27)
  I.9. #1, 2, 4, 5, 6, 8. I.10. # 1, 2, 3. [ Problem Set I.9. ] [ Problem Set I.10. ] [ Sample solution. ]
• Homework 8. (Due 2:00 p.m. April 3. )
  I.10. # 4, 6, 7, 8. I.11. # 1, 3, 10, 12. [ Sample solution. ]
  Extra credit. Use the norm in 1.11. (10). Show that (A,B) =||A|| ||B|| is nonzero if and only if $A$ and $B$ are multiple of each other.
  [ Problem Set I.10. ] [ Problem Set I.11. ]
• Homework 9. (Due 2:00 p.m. April 10. )
  I.12. # 1, 2, 3, 4. [ Problem Set I.12. ] [ Sample solution.]
• Homework 10. (Due 2:00 p.m. April 17.)
  III.1. # 1 -- 10. [ Problem Set III.1-1. ] [ Problem Set III.1-2. ] [ Sample solution.]
• Homework 11. (Due 2:00 p.m. April 24. )
  Problem Set III.2 #1 -10. [ Problem Set III.2. ] [ Sample Solution.]
• Homework 12. (Due 2:00 p.m. April 31. )
  Problem Set III.3 #1-6, 8. III.5 # 1,2. [ Problem Set III.3. ] [ Problem Set III.5. ] [ Sample Solution.]