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Math 307-101:
(0) Announcements
(1) Card Shuffling from "6 x 6" to "3 x 3"
Sections 0.0 and 0.1.
(2) Diagonalize [1/2,1/3;1/2,2/3] (HW 1)
you should make sure that you can do
this with any reasonable 2 x 2
matrix.
(3) Material will be added between
Sections 0.1 and 0.2 to help you
with sample exam problems.
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Announcements:
(1) Homework #1 is set:
Problem 1 due Sept 16.
Problems 2-6 due Sept 16,
unless ugrad lab accounts
delayed further.
(2) Streamlined homework:
- Must be on 8.5 x 11
- Must be stapled upper left
- Must have first three
letters of last name in
clear, block letters
- Handed into envelopes
by group
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Card Shuffling
- Card Shuffling leads to Markov matrices
- It is, at times, possible to work
with smaller matrices
- Start with three cards, A,B,C (6 x 6)
- Reduce in two ways to (3 x 3)
- Symmetry after first step
- Replace A,B,C with A,B,B
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- We need to "review"
- Markov matrices
- Given (Markov) matrix, A
how "to find" A, A^2, A^3,...
A^infinity
i.e., limit as n-> infty
of A^n
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- Review:
Eigenvalues and eigenvectors
(I make most of my living from them)
- Start from first homework problem:
- Diagonalize
A = [ 1/2,1/3 ; 1/2,2/3 ]
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