# Eigenvector calculation

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Kamuran on 24 Jan 2011
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)
Matthew Simoneau on 25 Jan 2011
If you display these numbers in hex format, you should be able to copy and paste them without loss.
format hex

Ned Gulley on 25 Jan 2011
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
##### 2 CommentsShowHide 1 older comment
Bruno Luong on 25 Jan 2011
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.

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