We will study the properties of matrices from a rigorous theoretical perspective. The goal of this course is to develop a deep intuition for matrices and linear transformations that will make applications of matrices to areas such as linear regression, computer graphics, and game theory seem natural.
The schedule below is tentative, and may be subject to change. Changes will be announced in class, and you are responsible for knowing about any changes even if you miss the class when they are announced.
| Week | Dates | Topic | Homework |
|---|---|---|---|
| 1 | Jan 14-18 | Inner products & norms | HW1 |
| 2 | Jan 21-25 | The characteristic polynomial | HW2 |
| 3 | Jan 28-Feb 1 | Similarity | HW3 |
| 4 | Feb 4-8 | Eigenvectors | HW4 |
| 5 | Feb 11-15 | Unitary matrices | HW5 |
| 6 | Feb 18-22 | Unitary equivalence theorem | |
| 7 | Feb 25-Mar 1 | Schur's triangularization | HW6 |
| 8 | Mar 4-8 | Normal matrices | HW7 |
| 9 | Mar 18-22 | Hermitian & symmetric matrices | HW8 |
| 10 | Mar 25-29 | The numerical range | HW9 |
| 11 | Apr 1-5 | Positive definite matrices | HW10 |
| 12 | Apr 8-12 | Singular value decomposition | HW11 |
| 13 | Apr 15-19 | Jordan canonical form | |
| 14 | Apr 22-26 | The minimal polynomial | HW12 |
Grades for this course will be determined by the percent of assigned problems completed. All homework problems will be graded on the following two point scale:
Score 2: This solution is correct. If there are any mistakes, they are minor typos that can be easily fixed.
Score 0: There is no solution. This is the default grade for any problem that has not been submitted.
To get an A in the class, you must have at least a score of at leasts 1 on 90% of all assigned problems, and 80% of problems should have a score of 2. To get a B in the class, you must have a 1 on 75% of all assigned problems and a 2 on 60%. To get a C you must have a 1 on 60% of all assigned problems and a 2 on 40%. You are allowed to resubmit problems as many times as needed until you solve them.