MATLAB: Eigenvector calculation

eigeigenvectorMATLAB

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)

Best Answer

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
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