Math 408/508: Advanced Linear Algebra Fall 2023

Instructor: Chi-Kwong Li

Meeting time and place: TT 12:30 - 1:50 p.m. Boswell 37
Office: Jones 128, Tel: 221-2042
E-mail: ckli@math.wm.edu, http://cklixx.people.wm.edu
Office hours: TR 2:00-4:00 p.m. Wed. 9:00- 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 future study and applications different topics such as Date science, AI, Quantum computing. You may share your views on the blackboard site why one need study advanced linear algebra, and what applications require the use of linear algebra.
This course will cover a list of topics including:

• Canonical forms (including Schur Triangular form, SVD, Jordan form etc.), which are very useful in 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.

• R. Bhatia, Matrix Analysis, Springer.
• S.R. Gracia and R.A. Horn, Matrix Mathematics, Cambridge Mathematical Textbooks, Cambridge University Press.
• R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press.
• G. Strang, Linear Algebra and its Applications, Thompson Brooks/Cole.
• G. Strang, Linear Algebra and Learning from Data, WELLESLEY-CAMBRIDGE PRESS.
• F. Zhang, Matrix theory: Basic results and techniques, Springer.

Homework will be assigned every week and due on Sunday (11:59 pm.) except for this week and the exam weeks.
Homework help sessions will be conducted on Thursday, 3:00-: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, or use Overleaf.

Challenging problems will be assigned from time to time;
extra-credits will be given to successful (or partially successful) attempts.

 
                 Homework   Exam. 1.   Exam. 2.      Final  
                 (weekly)   (Oct. 5)  (Nov. 16)     (Dec. 18, 9:00am.- noon)
                                                   
                   25%       20%       20%          35%

   
     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
        
               (Extra credits  may add another 5%)

Class notes (Under continuous revision)

• Notes.

• Homework 1. Will be posted soon. Due: Sept. 10, Sunday 11:59 p.m. Scan and submit your solution to blackboard.