Math 309: Intermediate Linear Algebra,
Spring 2020
Instructor: ChiKwong Li
Meeting time and place: TT 9:30  10:50 a.m. Jones 301
Office: Jones 128, Tel: 2212042
Email: 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 AMSMAA 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, 11:00noon 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;
extracredits will be given to successful (or partially successful)
attempts.
You have to use LaTex to typset mathematical document.
LaTex
Assessment
Exams: Midterm 1 Feb. 27 1:20 hrs (9:3011:50)
Midterm 2 April 2 1:20 hrs (9:3011:50)
Final May 13 3 hrs (9:00noon)
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 Midterm I Midterm 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.1I.9.
[
Scanned note on Lecutre on Jan 23, 2020. ]
[
Scanned note on Lecutre on Jan 28, 2020. ]
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Scanned note on Lecutre on Jan 30, 2020. ]
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Scanned note on Lecutre on Feb. 4, 2020. ]
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Scanned note on Lecutre on Feb. 6, 2020. ]
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Scanned note on Lecutre on Feb. 11, 2020. ]
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Scanned note on Lecutre on Feb. 13, 2020. ]
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Scanned note on Lecutre on Feb. 18, 2020. ]
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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. 2021.]
[
Scanned note on Lecutre on March 5, 2020. ]

Notes on I.9  I12 and after used in the Zoom meetings.

Notes on Secton III.
Homework list
 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.
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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.
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Problem Set III.11. ]
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Problem Set III.12. ]
[
Sample solution.]
 Homework 11. (Due 2:00 p.m. April 24. )
Problem Set III.2 #1 10.
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Problem Set III.2. ]
[
Sample Solution.]
 Homework 12. (Due 2:00 p.m. April 31. )
Problem Set III.3 #16, 8. III.5 # 1,2.
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Problem Set III.3. ]
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Problem Set III.5. ]
[
Sample Solution.]