%The program deals with a 5X5 state transition matrix

% of a reducible Markov chain.

%

%Original transition matrix is P1:

P1 = [0.5 0 0 0 0.5;

0 0.5 0 0.25 0

0 0 1 0.25 0

0 0.5 0 0.25 0

0.5 0 0 0.25 0.5]

[x1,d1] = eig(P1)

%Rearranged transition matrix

P2 = [1 0 0 0.25 0;

0 0.5 0.5 0 0

0 0.5 0.5 0.25 0

0 0 0 0.25 0.5

0 0 0 0.25 0.25]

[x2,d2] = eig(P2)

U1=P2(1,1)

[xu1,du1] = eig(U1)

U2=P2(2:3,2:3)

[xu2,du2] = eig(U2)

V=P2(4:5,4:5)

[xv,dv] = eig(V)