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Today:
Similar matrices: A and B are similar
if B = P^(-1) A P . Then
B^n = P^(-1) A^n P
for any n. (See Wikipedia: Matrix
similarity)
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.
For an algorithm, see 3,000 Solved ...,
Section 16.3.
Markov or stochastic matrices.
See also Subsections 4.6.1 and 4.6.2.
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Announcements:
Homework #1 is set:
Problem 1 due Sept 16.
Problems 2-6 due one week
from when ugrad lab accounts
are set up.
Please hand in Probs 2-6 on
Sept 16 if you can.
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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