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

## Daily outline for Fri, Sep 30, 2016 9:10 AM (1 year ago)

### Diagonalization

assigned today:
• standard-Diagonalization:

I can diagonalize a matrix and show and explain its usefulness.

1. any of the problems from 8.4.17-23.
2. 8.4.14. Also find the matrix raised to the 10th power.
• hint: there's a connection to the diagonalized version to raised to the 10th power.
3. Show how diagonalization helps understand example 4 on page 332.

Due 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.

# planning

• types of matrices
• symmetric
• orthogonal
• Hermitian
• unitary
• benefits of diagonalization
• powers
• no cross terms
• how to diagonalize
• prove that eigenvectors and eigen values are useful

# in class

• quiz on 2x2 (eigenvectors, values, how to hunt for them graphically)
• Markov problem raised to the 10th power
• ugh for 3x3
• Diagonalization
• didn't prove theorem 4 but we used it