# Mathematical and Computational Methods in Physics and Engineering (fall 2016)

## Daily outline for Wed, Sep 28, 2016 9:10 AM (1 year ago)

### Eigenvectors and eigenvalues

assigned today:
• standard-eigenvalues and eigenvectors:

I can describe, calculate, and use eigenvalues and eigenvectors.

1. Find a 2x2 matrix with real eigenvectors and values. Show how to calculate them and demonstrate what they mean geometrically using the Mathematica code we developed in lab.
2. Find the steady state for a 3-dimensional Markov problem. Tell the story as well.
3. Replicate example 8.4 (on page 332) where the problem is horizontal with a third spring tied from the last mass to a new wall.

Due today:

# in class

• quiz: equation for a plane
• I gave some hints before the quiz started
• find a 2x2 markov matrix
• find an (x,y) that won't be changed
• some changed their matrix {{0.5,0.5},{0.5,0.5}} is easy, for example
• Tom started right away with eigenvector stuff
• talked about the homogeneous way of thinking about it (det(A-lambda I)) etc
• talked about how it'll be a polynomial of order equal to the dimension of the matrix
• solved for the Markov ones and always got 1 and something else
• talked about how to get the eigenvector by plugging back in
• didn't really have time to talk about the spring example

edit