Math 223: Linear Algebra

Winter Term 2020
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 (clarification added 17/1) (LyX, TeX), due 18/1/2021. Solutions.
  2. Problem Set 2 (LyX, TeX), due 25/1/2021. Solutions.
  3. Problem Set 3 (LyX, TeX), due 1/2/2021. Solutions.
  4. Problem Set 4 (problem 5 fixed 4/2) (LyX, TeX), due 8/2/2021. Solutions.
  5. Problem Set 5 (LyX, TeX), due 22/2/2021. Solutions.
  6. Problem Set 6 (LyX, TeX), due 1/3/2021. Solutions.
  7. Problem Set 7 (LyX, TeX), due 8/3/2021. Solutions.
  8. Practice Problem Set 8 , not for submission. Solutions.
  9. Problem Set 9 (LyX, TeX), (typos in problem 3(d),7(d) corrected; phrasing of problems 7,8 improved) due 22/3/2021. Solutions.
  10. Problem Set 10 (LyX, TeX), due 29/3/2021. Solutions.
  11. Problem Set 11 (LyX, TeX), due 7/4/2021. Solutions.
  12. Problem Set 12 (LyX, TeX), due 14/4/2021. Solutions.

Lecture-by-Lecture information

We give section numbers in the textbook [1]; page numbers in the textbook [4]. 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 Scan Notes
F–I–S Axler
1 M 11/1 Introduction: Linearity     Scan slides handout
W 13/1 Vector spaces §1.2 pp. 4-12 Scan  
F 15/1 Subspaces §1.3 p. 13 Scan  
2 M 18/1 Linear combinations §1.4 p. 22 Scan PS1 due
W 20/1 Linear independence §1.5 pp. 22-27 Scan  
F 22/1 Bases §1.6 pp. 27-31 Scan  
3 M 25/1 Dimension   pp. 31-34 Scan PS2 due
W 27/1 Geometry     Scan  
F 29/1 Linear maps §2.1 pp. 37-41 Scan  
4 M 1/2 Kernel and image   pp. 41-47 Scan PS3 due
W 3/2 Matrices §2.2 pp. 48-50 Scan  
F 5/2 Midterm 1       Info
5 M 8/2 Midterm review     Scan PS4 due
W 10/2 Matrix multiplication §2.3 pp. 50-53 Scan  
F 12/2 Linear equations §3.3   Scan  
6 M 22/2 Gaussian Elimination §3.1, §§3.3-4   Scan PS5 due
W 24/2 (continued)     Scan  
F 26/2 Determinants §§4.1-3 pp. 225-236 Scan  
7 M 1/3 (continued)     Scan PS6 due
W 3/3 Determinants, Again §4.5   Scan  
F 5/3 (continued)     Scan  
8 M 8/3 Similarity §2.5   Scan PS7 due
W 10/3 Eigenvalues §5.1 pp. 75-79 Scan  
F 12/3 Midterm 2        
9 M 15/3 Midterm review     Scan  (no PS8)
W 17/3 Multiplicity     Scan  
F 19/3 Multiplicity   pp. 87-90 Scan  
10 M 22/3 Diagonalization §5.2   Scan PS9 due
W 24/3 Application     Scan  
F 26/3 Inner product spaces §6.1 Ch. 6 Scan  
11 M 29/3 Cauchy--Schwartz     Scan PS10 due
W 31/3 Gram--Schmidt     Scan  
W 7/4 Orthogonality     Scan PS11 due
12 F 9/4 The Adjoint §6.4 pp. 127-137 Scan  
M 12/4 The Spectral Theorem     Scan  
W 14/4 (continued)     Scan PS12 due
  W 29/4 Final Exam: 8:30am-11am        


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Last modified Monday April 26, 2021