# Linear II Online Presentations

As we all know, a shifting reality has forced us to move to remote teaching for the rest of the semester. This web page complements our existing class web page and coordinates the online materials I'm developing to get us through this. You should also check out our revised syllabus.

The biggest addition to the course is a series of online presentations I'm developing to disseminate the material. These should be viewable in any reasonably new web browser or even on a tablet or smart phone. Please alert me to any difficulties as soon as you encounter them!

Note that the presentations linked on this page are asynchronous - i.e., you go through them at a time that works for you. In addition to the presentations, I'm planning on holding online office hours during the first half of our regularly scheduled class hours. I will email you a standing Google Meet link to access that.

## Outline

• Monday, March 23: Intro to the new tools
• Overview
Today, we're going to ease back into the new reality by just getting acquainted with some of our new tools and going over the new expectations. Jump into the Presentation on presentations link below to get started.
• The Presentation presentation
• Assignments
Again, the main goal for now is to acquaint ourselves with some new tools and to make sure that we can use the old remotely. To that end, If you are interested in reading ahead at all, I'm sure we'll be jumping in to sections 8.2 and 8.3 on Wednesday - particularly, the portion in 8.3 on diagonalization.
• Wednesday, March 25: Eigenvalues, Eigenvectors, and diagonalization
• Overview
As this is a second course in linear algebra, everyone should have some experience with eigenvalues and eigenvectors. In this presentation, we'll talk about how we use eigenvalues and eigenvectors to find the diagonalization of a matrix, provided some nice conditions are satisfied.
Much of this material is taken from section 8.3 of our text, particularly the last part on diagonalization.
• Presentation
• Problems
I've got one good forum problem for you: Your mission is simply going to be to diagonalize a matrix. I've got a randomly generated matrix for each of you and you can find your by choosing your forum login name from the following list:
Once you've got your matrix, respond to this forum question to explain how to diagonalize it.
• Monday, March 30: Complex Eigenvalues
• Overview
What do we do when a matrix has complex eigenvalues? How do we compute with them and what do they tell us?
It turns out that they're not that hard to compute with at all and they tell us that the geometric action of the matrix includes rotation. In addition, proper treatment of complex eigenvalues greatly the class of diagonalizable matrices allowing us to apply everything we learned about diagonalization.
• Presentation
• Problems
We've got two 10 point forum problems this week. In the first, you'll find a 3D rotation about a randomly generated vector and in the second, you'll find the geometric action of a randomly generated matrix.
Problem 1: In this problem, you'll find a 3D rotation about a randomly generated vector. The problem is completely spelled out in this forum post.

Problem 2: In this problem, you're going to describe the geometric action of a matrix with complex eigenvalues using the eigenstructure of the matrix. You should get your matrix using the pull-down menu below and then answer the question by responding to this forum post.
• Monday, April 6
• Overview
Today, we'll talk about the power method and how it can be used to compute complex eigenvectors and associated eigenvalues.
This material appears in much more detail in sections 9.1 and 9.5 of our text.
• Presentation
• Problems
There's just one problem on this material - namely, revisit your eigenranking computation using the power method. You can do it by answering this forum question.
There is more to do with this stuff as briefly mentioned on our the last slide of the power method presentation. I anticipate a more substantive programming project involving that material next time.
• Monday, April 13:
• Monday, April 13: Self-similarity
• Overview
Today, we're going shift to a fun topic where linear algebra is applied a lot, namely fractal geometry.
• Presentation
• Assignment
• There is one forum based assignment; you can get yours by choosing your forum login name from this menu: