Eigenvector calculation

I am trying to calculate the eigenvectors and eigenvalues for the following matrix (6,6) and I am getting complex eigenvector which I should not. I check the eigenvectors with maple and no complex eigenvector. Can anyone help me? ( complex numbers are not small. There on the same order or real ones)

-30.400000000000009  20.099689437998496  16.988854381999836 -12.099689437998487  13.411145618000168  -7.999999999999998
-1.105572809000086  -3.811145618000166   4.683281572999748   1.105572809000084  -3.577708763999662   2.705572809000083
 4.494427190999916  -0.683281572999748  -7.388854381999832   3.577708763999663   2.894427190999915  -2.894427190999915
-2.894427190999916   2.894427190999916   3.577708763999664  -7.388854381999831  -0.683281572999745   4.494427190999913
 2.705572809000084  -3.577708763999665   1.105572809000085   4.683281572999745  -3.811145618000171  -1.105572809000080
-7.999999999999998  13.411145618000166 -12.099689437998482  16.988854381999822  20.099689437998467 -30.399999999999970

You can see that the first 3 row almost a mirror image of last 3 (or vice versa). Actually it has to be to same, but due to around offs coming from calculation creates 10^-13 differences. If I make those changes and makes them excatly mirror images no complex eigenvectors (which is little odd)

[Kenneth Eaton]

As Bruno Luong pointed out in a comment on my now-deleted answer, to help you we would need the exact numerical values in your matrix. The above values are likely truncated for display purposes.

[Kamuran]

I edti the exact numbers. I know this does not look nice but this zqs the only way for me to fit those numbers. Thank you for your help.

[Matthew Simoneau]

If you display these numbers in hex format, you should be able to copy and paste them without loss.

format hex

[Naveed Ahmed]

and the matrix should always be 'Square' to get the eigean vectors.

[Torsten]

@Naveed Ahmed

How should A*x = lambda*x hold if A were not square ?

Answer 1

[Ned Gulley]

When I run the eig command (see help here: eig) I don't get any complex eigenvectors. Maybe the problem is data entry?

Assuming your matrix is in a, then

[v,d] = eig(a)

v =

     -0.7059   -0.6622    0.4830    0.3203   -0.0000    0.4644
      0.0294   -0.1076    0.4654   -0.4804    0.5774    0.4425
      0.0294    0.2235    0.2239    0.3203   -0.0000   -0.2974
      0.0294   -0.2235   -0.2239   -0.4804    0.5774   -0.2974
      0.0294    0.1076   -0.4654    0.3203   -0.0000    0.4425
     -0.7059    0.6622   -0.4830   -0.4804    0.5774    0.4644
d =

    -40.0000         0         0         0         0         0
           0  -31.1332         0         0         0         0
           0         0   -2.4668         0         0         0
           0         0         0    0.0000         0         0
           0         0         0         0   -0.0000         0
           0         0         0         0         0   -9.6000

[Kamuran]

There is a problem for sure. Because I do not think I can enter all the digits in here. When I copy the matrix from here and input that into matlab, there is a difference between my actual matrix and this one. The largest difference is 10^-15 but that causes the problem. Is there any way I can upload my matlab file here?

[Bruno Luong]

You might try free host servers, but as I have pointed out earlier, the smallest eigen values are 1e-17 of the largest, so any small perturbation of matrix elements could easily make smallest eigen value becomes complex. That's not a surprise to me. You might need to make some safeguard code against this issue.

[Christine Tobler]

Yes, you can attach a .mat file (look for the little "attachment button" when editing the post - like a paperclip).

For this small matrix, here's a way you can display it so that there are no differences:

for ii=1:size(A, 1)
s(ii) = string(sprintf('%.20e ', A(ii, :)));
end
disp("Acopy = [" + join(s, ";"+newline) + "]")

Run this code where you have the original matrix A, then use isequal(A, Acopy) to verify it matches exactly.