Result of A(:,:,1,1) coming as result of A(:,:,1,2)

Hello,

Ihave this code:

function [A,B] = trying(d)
A=zeros(d,d,2,d);    
sigma_x = [0,1;1,0];
sigma_z = [1,0;0,-1];
if d==2
   x = sigma_x;
   z = sigma_z;
end
if d==4
    x = kron(sigma_x,sigma_x);
    z = kron(sigma_z,sigma_z);
end
[xv1,xv2] = eig(x);
%xv1 = [xv1(:,2),xv1(:,1)];
[zv1,zv2] = eig(z);
%zv1 = [zv1(:,2),zv1(:,1)];
   for i=1:d
%       for k = 1:2
           A(:,:,1,i)= xv1(:,i)*transpose(xv1(:,i));
           A(:,:,2,i)= zv1(:,i)*transpose(zv1(:,i));
      
%       end
   end
end

However, I have inverse result For instance the result should be like that:

A(:,:,1,1) =

    0.5000    0.5000
    0.5000    0.5000


A(:,:,2,1) =

     1     0
     0     1


A(:,:,1,2) =

    0.5000    -0.5000
   -0.5000    0.5000

But I have this result:

   A(:,:,1,1) =

    0.5000   -0.5000
   -0.5000    0.5000


A(:,:,2,1) =

     0     0
     0     1


A(:,:,1,2) =

    0.5000    0.5000
    0.5000    0.5000

So I tried the that But it did not work

xv1 = [xv1(:,2),xv1(:,1)];
zv1 = [zv1(:,2),zv1(:,1)];
for i=1:d
    for k = 1:2
           A(:,:,1,i)= xv1(:,k)*transpose(xv1(:,k));
           A(:,:,2,i)= zv1(:,k)*transpose(zv1(:,k));
    end
end

Any idea?

[Geoff Hayes]

Gözde - why should the output look like the first block of output that you have shown? What algorithm or equations are you basing your code on? Also, note the following

   for i=1:d
%       for k = 1:2
           A(:,:,1,i)= xv1(:,i)*transpose(xv1(:,i));
           A(:,:,2,i)= zv1(:,i)*transpose(zv1(:,i));
      
%       end
   end

Since i is either 1 or 2, then this means that you also have A(:,:,2,2) set with a value which in this case is

   A(:,:,2,2) =

     1     0
     0     0

Is this expected or should you just have populated A(:,:1,1), A(:,:,1,2), and A(:,:,2,1)?

[Gözde Üstün]

Hello,

Because I am using "eig" function and in the eig function, first eigenvector is coming as second eigen vector.

You are right I (should) have also A(:,:,2,2) but for showing you I just put the other values.

Answer 1

[Christine Tobler]

The eigenvectors returned by EIG are returned in the same order as the eigenvalues, but the eigenvalues are not necessarily sorted. Could this be the issue here?

[Gözde Üstün]

Yeah How can I solve this prolem? I used that:

xv1 = [xv1(:,2),xv1(:,1)];
zv1 = [zv1(:,2),zv1(:,1)];
for i=1:d
    for k = 1:2
           A(:,:,1,i)= xv1(:,k)*transpose(xv1(:,k));
           A(:,:,2,i)= zv1(:,k)*transpose(zv1(:,k));
    end
end

But it did not work for me

[Christine Tobler]

You can sort the eigenvalues and eigenvectors before using them further, see this example for how to do that.