Math 223: Linear Algebra

Winter Term 2021
Lior Silberman

General Information

References

  1. Friedberg, Insel and Spence, Linear Algebra, Pearson.
  2. Lipschutz, Schaum's Outline of Linear Algebra, McGraw-Hill.
  3. Halmos, Finite-dimensional Vector Spaces, Springer.
  4. Axler, Linear Algebra Done Right, Springer.

Exams

Problem Sets

  1. Problem Set 1 (LyX, TeX), due 20/1/2022 (questions 1(b),3,5 clarified). Solutions.
  2. Problem Set 2 (LyX, TeX), due 26/1/2022 (typos in 4(b),4(d) fixed).

Lecture-by-Lecture information

It is crucial to read the relevant material ahead of each lecture in order to properly participate and learn. The goal is not to master the material but to learn the new vocabulary and see how the concepts hang together.

The table gives section numbers in the textbook [1] and page numbers in the textbook [4], but you should feel free to read any book on the topic. A precis of the material also appears in the course notes.

Warning: the following information is tentative and subject to change at any time

Week Date Material Reading Recap Notes
F–I–S Axler
1 M 10/1 Introduction: Linearity     Scan slides handout
W 12/1 Vector spaces §1.2 pp. 4-12 Scan  
F 14/1 Subspaces §1.3 p. 13 Scan  
2 M 17/1 Linear combinations §1.4 p. 22 Scan
Video
PS1 due
W 19/1 Linear independence §1.5 pp. 22-27 Scan  
F 21/1 Bases §1.6 pp. 27-31 Scan  
3 M 24/1 Dimension   pp. 31-34 Scan  
W 26/1 Geometry     PS2 due
F 28/1 Linear maps §2.1 pp. 37-41  
4 M 31/1 Kernel and image   pp. 41-47  
W 2/2 Matrices §2.2 pp. 48-50 PS3 due
F 4/2 Matrix multiplication §2.3 pp. 50-53  
5 M 7/2 Midterm 1       Info
W 9/2 Midterm review     PS4 due
F 11/2 Linear equations §3.3    
6 M 14/2 Gaussian Elimination §3.1, §§3.3-4    
W 16/2 (continued)     PS5 due
F 18/2 Determinants §§4.1-3 pp. 225-236  
21/2-27/2            
7 M 28/2 (continued)     PS6 due
W 2/3 Determinants, Again §4.5    
F 4/3 (continued)      
8 M 7/3 Similarity §2.5   PS7 due
W 9/3 Eigenvalues §5.1 pp. 75-79  
F 11/3 Midterm 2        
9 M 14/3 Midterm review     PS8 due
W 16/3 Multiplicity      
F 18/3 Multiplicity   pp. 87-90  
10 M 21/3 Diagonalization §5.2   PS9 due
W 23/3 Application      
F 25/3 Inner product spaces §6.1 Ch. 6  
11 M 28/3 Cauchy--Schwartz     PS10 due
W 30/3 Gram--Schmidt      
F 1/4 Orthogonality      
12 M 4/4 The Adjoint §6.4 pp. 127-137 PS11 due
W 6/4 The Spectral Theorem      
F 8/4 (continued)     PS12 due
  TBA Final Exam: TBA        


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