Math 412: Advanced Linear Algebra

Fall Term 2017
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

Midterm Exam

Problem Sets

  • Problem set grade statistics.
    1. Problem Set 1, due 14/9/2017. Solutions.
    2. Problem Set 2, due 21/9/2017 (typo in 5(b) corrected). Solutions (Solution to 5(a) fixed).
    3. Problem Set 3, due 28/9/2017. Solutions.
    4. Problem Set 4, due 5/10/2017. Solutions.
    5. Problem Set 5, due 12/10/2017. Solutions.
    6. Problem Set 6, due 26/10/2017. Solutions.
    7. Problem Set 7, due 2/11/2017. Solutions.
    8. Problem Set 8, due 9/11/2017. Solutions.
    9. Problem Set 9, due 16/11/2017.
    10. Problem Set 10, due 23/11/2017.

    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 Th 7/9 Introduction §1,§2  
    2 T 12/9 Direct sum and product §19,§20 Note on infinite dimensions
    Th 14/9 (continued)   PS1 due
    3 T 19/9 Quotients §21,§22  
    Th 21/9 Duality §13,§15 PS2 due
    4 T 26/9 Bilinear forms
    Tensor Products
    §23
    §24,§25
     
    Th 28/9 (continued)    
    5 T 3/10 \Sym^n and \wedge^n §29,§30  
    Th 5/10 (continued)   PS4 due; Feedback form
    6 T 10/10 Motivation
    The minimal polynomial
    N2.1
    N2.2
     
    Th 12/10 Generalized eigenspaces N2.3 PS5 due
    7 T 17/10 Cayley--Hamilton
    Jordan Blocks
    N 2.3
    §57, N 2.4
     
    Th 19/10 Midterm exam    
    8 T 24/10 Nilpotent Jordan form
    Jordan canonical form
    §57, N 2.4
    §58, N 2.5
     
    Th 26/10 Vector Norms §86, N 3.1 PS6 due
    9 T 31/10 Matrix Norms
    Power Method
    §87, N 3.2
    N 3.3
     
    Th 2/11 Completeness N 3.4 PS7 due
    10 T 7/11 Series N 3.4  
    Th 9/11 Power series
    The Resolvent
    N 3.5
    N 3.6
    PS8 due
    11 T 14/11 Holomorphic calculus N 3.7  
    Th 16/11 Composition N 3.7 PS9 due
    12 T 21/11      
    Th 23/11     PS10 due
    13 T 28/11      
    Th 30/11 Review    
      TBA Final exam    


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    Last modified Thursday November 09, 2017