Math 490 - Spring 2019


Basic Info

Course Description

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.

Tentative Schedule

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  

Grading Policy

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:

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.