Markov processing and Eigenvectors

Hello I am trying to compute the eigenvectors and eigenvalues of the transition matrix . And plot the limiting distribution

And here my attempt to solve it.

I could not got the correct eignvalue and the correct plot. I think I need to normalize it but it's not work with me.

Thaks in advance!

input=fileread('amino.txt');
Amino=['A', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'K', 'L', 'M', 'N', 'P', 'Q', 'R', 'S', 'T', 'V', 'W', 'Y', '$'];
Amino=Amino';
n=size(Amino);
total=0;
for i=1:size(Amino)
    List(i)=length(strfind(input,Amino(i)));
    
end
List=List';


%normalize
% List_sum=sum(List);
% for i=1:size(List)
%     List(i)=List(i)/List_sum;
%     
% end

for i=1:size(Amino)
    for j=1:size(Amino)
        f=strcat(Amino(i),Amino(j))
        result(j,i)= length(strfind(input,strcat (Amino(i),Amino(j))))/List(i);
    end
end


% normalize
List_sum=sum(List);
for i=1:size(List)
    List(i)=List(i)/List_sum;
    
 end

Cond_prob=0;
for i=1:length(result)
    Calc_ent=0;
    for j=1:length(result)
        Calc_ent=Calc_ent+result(j,i)*log2(result(j,i));
    end
    Cond_prob=Cond_prob+res(i)*Calc_ent;
end
Cond_prob=-Cond_prob;
    
   
    
 

[Walter Roberson]

See also user question at https://www.mathworks.com/matlabcentral/answers/482005-probability-of-markov-process

[Brave A]

?

Answer 1

[Brave A]

Any thoughts?