Can I plot eigenvalues corresponding to certain eigenvectors?

Hello everyone!

I've got a matrix 4x4 with with some kind of functions as a matrix elements. I would like to plot eigenvalues corresponding to certain eigenvector, in my case (-1 0 0 1). My idea is something like that (part of the code):

[vec,val]=eig(matrix);

       for n=1:4

       c=vec(:,n);

           if c(1)+c(4)==0 && c(1)~=0 && c(4)~=0

             y=loglog(w,(val(n,n));
             hold on;

          end
      end

It seems that loop with element 'c=vec(:,n)' is not sufficient for the case, as Matlab draws only a few points (for sure too few). What I would like to get: first loop (n=1:4) takes each of eigenvector of the system, and then (second loop) draws only those eigenvalues, which corresponds to the statements given as in the code above. Any idea how to fix my code?

Any help appreciated!

Answer 1

[Bjorn Gustavsson]

Well first you have to remember that the eigenvectors doesn't necessarily exactly match your desired one, so you'll have to be prepared to save away that deviation too.

Perhaps something along:

[vec,val]=eig(matrix);
target_vec = [-1 0 0 1];
[mostParallel,idxBest] = max(abs(vec*target_vec'));
Lambda_mostParallel = val(idxBest,idxBest);

HTH

[Pawel Rochowski]

Thank you for the answer. I checked the system - as you pointed out, the values of eigenvectors elements vary a little bit. So that was my problem. Your method improved my calculus, but still I was getting problems, since other vectors are 'more' parallel to target vector than [-1 0 0 1] (by 'more; I understand the first found vector with elements [-a 0 0 b] a>0 b>0) :) So I decided to use an eigenvectors matrix property which I did not mentioned before, that absolute values of vector elements for which I want to plot eigenvalues are the biggest one in rows 1 and 4. Nevertheless, thanks for response and time!