Math 19b: Linear Algebra with Probability Oliver Knill, Spring 2011
Lecture 27: Discrete dynamical systems
1Choose 4 random numbers between 1 and 6.
A B C D
If the vector is e1, then only go down if the number is 1 otherwise, go
up. If the vector is e2, then go down if the number is odd, otherwise,
go up.
We now find experimentally the eigenvector of the Markov matrix
A=
5/6 1/2
1/6 1/2
to the eigenvalue 1 in class.
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1