CODEWITHSUNDEEP
matlabmatheigenvalue
user3650942
user3650942

Reputation: 41

How can I plot only real eigenvalues of symmetrical matrix in matlab?

I have created a matrix of potentials for a particle in a square well. When I take the eigenvectors of the matrix, I get mirror images for the first few (about 10) vectors. For example, the first eigenvector is a postive hump but there is also a negative mirror hump underneath. I looked at the output of the first few vectors and it appeared that the sign of the number was merely changing back and forth from positive to negative. For later vectors this is not the case so I cannot just plot every other point of the vectors. I am using the following command to plot eigenvectors.

[V,D] = eig(A);

I do not see imaginary numbers in my output. However, it has been suggested to me that MATLAB may be trying to plot the real and imaginary components of the eigenvectors. I found the following command on this site and thought it would fix my problem assuming my problem is in fact that the real and imaginary components are not being plotted.

A1 = real(V*real(D)/V);

then I plot:

[V,D] = eig(A1);

Nothing has changed and I am confused as to whether I am correctly plotting the real eigenvalues or if there is something else causing these mirror images. Help!

Upvotes: 1

Views: 1320

Answers (1)

Lutz Lehmann
Lutz Lehmann

Reputation: 26040

Real symmetric matrices have always only real eigenvalues and orthogonal eigenspaces, i.e., one can always construct an orthonormal basis of eigenvectors.

If your physical system has a spacial symmetry, for instance if you can mirror it about some symmetry axis such that the physics of both systems is the same, then this symmetry is also reflected in the eigenspaces, they will always have even dimension and you can either construct odd and even symmetric eigenvectors or pairs of eigenvectors that are mirror images of each other.

To say more one needs more details about your problem.

Upvotes: 0

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