Math 412: Advanced Linear Algebra

Fall Term 2016
Lior Silberman

General Information

This is a second course in linear algebra, intended for honours students. There is no required textbook. The book by Halmos is very good, covers nearly everything, and is available in PDF form from the publisher for anyone on the UBC network; a lot of the material can also be found in any "abstract algebra" textbook. More details may be found in the syllabus.

References

  1. Halmos, Finite-dimensional Vector Spaces, available from SpringerLink
  2. Coleman, Calculus on Normed Vector Spaces, Chapter 1 (on SpringerLink)
  3. Higham, Functions of Matrices, available from SIAM
  4. [Your favorite author], Abstract Algebra

Final Exam

Midterm Exam

Problem Sets

  • Problem set grade statistics.
    1. Problem Set 1, due 14/9/2016. Solutions.
    2. Problem Set 2, due 21/9/2016. Solutions.
    3. Problem Set 3, due 28/9/2016 (added practice problem, clarification on P4, hint to 1(a)) Solutions.
    4. Problem Set 4, due 5/10/2016. Solutions.
    5. Problem Set 5, due 12/10/2016. Solutions.
    6. Problem Set 6, due 26/10/2016 (problem 2(c) clarified). Solutions.
    7. Problem Set 7, due 2/11/2016. Solutions.
    8. Problem Set 8, due 9/11/2016. Solutions.
    9. Problem Set 9, due 16/11/2016. Solutions.
    10. Problem Set 10, now due 30/11/2016. Solutions.

    For your edification

    Lecture-by-Lecture information

    Section numbers marked § are in Halmos [1], section numbers marked N are in the course notes above.

    Week Date Material Reading Notes
    1 W 7/9 Introduction §1,§2  
    F 9/9 Direct sum and product §19,§20 Note on infinite dimensions
    2 M 12/9 (continued)    
    W 14/9 (continued)   PS1 due
    F 16/9 Quotients §21,§22  
    3 M 19/9 Duality §13,§15  
    W 21/9 (continued)   PS2 due
    F 23/9 (continued)    
    4 M 26/9 Bilinear forms §23  
    W 28/9 Tensor products §24,§25 PS3 due, Note on categories
    F 30/9 (continued)    
    5 M 3/10 (continued)    
    W 5/10 \Sym^n and \wedge^n §29,§30 PS4 due; Feedback form
    F 7/10 (continued)    
    6 W 12/10 Motivation   PS5 due
    F 14/10 The minimal polynomial N 2.2  
    7 M 17/10 Generalized eigenspaces N 2.3  
    W 19/10 Midterm exam    
    F 21/10 Cayley--Hamilton N 2.3  
    8 M 24/10 Jordan Blocks §57, N 2.4  
    W 26/10 Nilpotent Jordan form §57, N 2.4 PS6 due
    F 28/10 Jordan canonical form §58, N 2.5  
    9 M 31/10 Vector Norms §86, N 3.1  
    W 2/11 Matrix Norms §87, N 3.2 PS7 due
    F 4/11 (continued)    
    10 M 7/11 Power method N 3.3  
    W 9/11 Completeness N 3.4 PS8 due
    11 M 14/11 Series N 3.4  
    W 16/11 Power series N 3.5 PS9 due
    F 18/11 The Resolvent N 3.6  
    12 M 21/11 Holomorphic calculus N 3.7  
    W 23/11 Composition N 3.7 PS10 due
    F 25/11      
    13 M 28/11      
    W 30/11     PS10 due
    F 2/12 Review    
      T 6/12 Final exam    
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    Last modified Saturday December 03, 2016