Math 412: Advanced Linear Algebra

Spring Term 2014
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

Problem Sets

  1. Problem Set 1, due 15/1/2014. Solutions.
  2. Problem Set 2, due 22/1/2014 (also as: LyX, LaTeX). Solutions.
  3. Problem Set 3, due 29/1/2014 [practice problems replaced] (also as: LyX, LaTeX). Solutions.
  4. Problem Set 4, due 7/2/2014. Solutions.
  5. Problem Set 5, due 14/2/2014 [problem 2 shortened; minor fixes in problems 1,4]. Solutions.
  6. Problem Set 6, due 28/2/2014. Solutions.
  7. Problem Set 7, due 10/3/2014 [problem 4 corrected]. Solutions.
  8. Problem Set 8, now due 19/3/2014 [calculational problem added]. Solutions.
  9. Problem Set 9, due 26/3/2014. Solutions.
  10. Problem Set 10, due 7/4/2014 [problems 4(b),4(c), 6(a) corrected]. Solutions.

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 M 6/1 Introduction §1,§2  
W 8/1 Direct sum and product §19,§20 Note on infinite dimensions
F 10/1 (continued)    
2 M 13/1 (continued)    
W 15/1 Quotients §21,§22 PS1 due
F 17/1 Duality §13,§15  
3 M 20/1 (continued)    
W 22/1 (continued)   PS2 due
F 24/1 Billinear forms §23  
4 M 27/1 Tensor products §24,§25 Note on categories
W 29/1 (continued)   PS3 due
F 31/1 Review    
5 M 3/2 \Sym^n and \wedge^n §29,§30  
W 5/2 (continued)    
F 7/2 Motivation   PS4 due; Feedback form
6 W 12/2 The minimal polynomial N 2.2.1  
F 14/2 Generalized eigenspaces N 2.2.2 PS5 due
  M 24/2 Midterm exam    
7 W 26/2 Algebraic closure N 2.2.3  
F 28/2 Nilpotence N 2.2.4 PS6 due
8 M 3/3 Jordan blocks N 2.2.4  
W 5/3 Nilpotent Jordan form N 2.2.4  
F 7/3 Jordan canonical form N 2.2.5  
9 M 10/3 Vector Norms §86, N 3.1 PS7 due
W 12/3 Matrix Norms §87, N 3.2  
F 14/3 (continued)    
10 M 17/3 Power method    
W 19/3 Completeness   PS8 due
F 21/3 Series    
10 M 24/3 Power series    
W 26/3 Holomorphic calculus   PS9 due
F 28/3 Composition    
12 M 31/3 The Resolvent    
W 2/4      
F 4/4      
13 M 7/4 Review   PS10 due
  M 16/4 Final exam    


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Last modified Friday May 02, 2014