Math 408: Advanced Linear Algebra
Fall 2016
Instructor: ChiKwong Li
Meeting time and place: TT 2:00  3:20 p.m. Jones 306
Office: Jones 128, Tel: 2212042
Email: ckli@math.wm.edu, http://cklixx.people.wm.edu
Office hours: TWR 9:00 a.m.  10:00 a.m. or by
appointments.
Course description:
The goal of the course is to equip students with the matrix techniques which can be
used in further study and applications.
You may consider also taking Math 41001 Applied Linear Algebra to explore more
current research and applied topics.
This course (Math 408) will cover a list of topics including:
 Canonical forms (including Jordan form, Schur Triangular form, SVD, etc.) and their applications.
 Special classes of matrices (normal matrices, Hermitian matrices, positive semidefinite matrices).
 Norms and matrix inequalities.
 Perron Frobenius theory on nonnegative matrices.
 Other topics: tensor products, numerical ranges, quantum computing.
The discussion will be based on classnotes. Here are some useful references:
 R. Bhatia, Matrix Analysis, Springer.
 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, 3:305:00 p.m. Jones 113 or 131.
Of course, help is also available at office hours.
You have to use LaTex to typset mathematical document,
an excellent skill to acquire. You may get the programs for free.
 For windows users,
(a) download the MikTex program from http://miktex.org/download;
(b) then download the Texmaker program from http://www.xm1math.net/texmaker/download.html;
(c) then open the program "texmaker";
(d) copy (or download and then open) the "homework01.tex" file to the texmaker window;
(e) select "LaTex" from the "Quick Build" menu;
(f) click the "=>" arrow on the left of "Quick Buil" to get the pdf output.

For Mac users,
(a) download MacTex from http://tug.org/mactex/;
(b) open the "texshop" program,
(c) copy (or download and then open) the "homework01.tex" file to the texshop window;
(d) change "PlainTex" to "LaTex" at "Typeset" menu;
(e) click "Typeset" icon to get the pdf output.
 You may also use the online editor
Write LaTeX .
 Here is
a list of TeX commands for mathematics symbols.
Challenging problems will be assigned from time to time;
extracredits will be given to successful (or partially successful)
attempts.
Assessment
Exams: Midterm Oct. 6 1:20 hrs (14:0015:20)
Final Dec. 7 3 hrs (14:0017:00)
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 Final
30% 30% 40%
(Extra credit problems may add up to another 5%)
Class notes (Under continuous revision)
Scans of hand written notes in the lectures
Homework list

Homework 1. Due Sept. 2, noon.
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Homework 2. Due Sept. 9, noon. (postponed to Sept. 12 (Monday), noon).
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Homework 3. Due Sept. 23 (Friday), noon).
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 Homework 4. Due Sept. 30 (Friday), noon).
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 Homework 5. Due: Oct. 18 (Tuesday), noon.
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 Homework 6. Due: Oct. 26 (Wed.), 5:00 pm.
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 Homework 7. Due: Nov. 4 (Fri.), noon.
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 Homework 8. Due: Nov. 16 (Wed), noon.
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 Homework 9. Due: Nov. 29, noon.
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Examination 1 (Take home). Due October 7 (Friday), noon).
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Final Examination (Take home). Due Dec. 8 (Thursday), noon).
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