Search and Rank Computations

-- Philip Yasskin

-- Texas A&M University

-- TAMU Math Circle

with(LinearAlgebra): Digits:=20:

Replace the xx's by the numbers in your Probability Transition Matrix:

M:=Matrix([ [ 0, xx, xx, xx, xx], [ xx, 0, xx, xx, xx], [ xx, xx, 0, xx, xx], [ xx, xx, xx, 0, xx], [ xx, xx, xx, xx, 0] ]);

Execute one of the following initial State Vectors.

S:=<1,0,0,0,0>;

S:=<0,1,0,0,0>;

S:=<0,0,1,0,0>;

S:=<0,0,0,1,0>;

S:=<0,0,0,0,1>;

Here is the state after 1 step:

M .S;

Here is the state after 2 steps:

M^2 .S;

Here is the state after 3 steps:

M^3 .S;

Here is the state after 100 steps:

M^100 .S;

Here it is converted to a decimal percent:

100*evalf(%);

Here is the state after 101 steps:

M^101 .S;

Here it is converted to a decimal percent:

100*evalf(%);

Notice the state after 100 or 101 steps is essentially the same . This is called s ateady state solution.

Notice the results are the same no matter which initial state you use.