How can I plot a graph for only one eigen value against a variable? I'm only getting one M!

I am trying to plot a graph for k:[0,1] against the larger eigenvalue from the corresponding matrix. i.e for each value of k I am only interested in the larger of the two eigenvalues from the 2x2 matrix M.

This is a very basic code, I know, but having played around with it for a few days now I could really use some help!

    % code
A=3.3;
B=0.45;
a=B;
b=((A+sqrt(A^2-4*B^2))/(2*B))^2;
c=-2*B;
d=-1-b;
D=500;
for k=0.0:0.01:1.0
    M=[a-k^2 b; c d-D*k^2];
    lam=eig(M);
end
plot(k,lam)
  end

Answer 1

[Akira Agata]

I have slightly modified your code. I hope this will help!

A=3.3;
B=0.45;
a=B;
b=((A+sqrt(A^2-4*B^2))/(2*B))^2;
c=-2*B;
d=-1-b;
D=500;

k = (0:0.01:1);
lam = zeros(2,length(k));

for kk = 1:length(k)
  M=[a-k(kk)^2 b; c d-D*k(kk)^2];
  lam(:,kk)=eig(M);
end
plot(k,lam)

[Jessica Wilcox]

Thank you for your comment. This produces a graph, but for both eigenvalues. What I am trying to do is plot only the larger of each eigenvalue, and wondered if there is a simple way to do this. Thanks again.

[Akira Agata]

Yes, that's a piece of cake!

Let me slightly modify the code again.

 A=3.3;
 B=0.45;
 a=B;
 b=((A+sqrt(A^2-4*B^2))/(2*B))^2;
 c=-2*B;
 d=-1-b;
 D=500;

 k = (0:0.01:1);
 lam = zeros(1,length(k));

 for kk = 1:length(k)
  M=[a-k(kk)^2 b; c d-D*k(kk)^2];
  lam(kk)=max(eig(M));
 end
 plot(k,lam)

Now, you can obtain a plot only the larger eigenvalue as a function of k.

[Jessica Wilcox]

Thank you, I have only just seen your reply - I had managed to work this bit out on my own but couldnt have gotten there without your edit, thank you!