# Eigenvector

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Hi, I'm trying to make a routine calculating eigenvalues and eigenvectors. The eigenvectors result of my program is a bit different from the result of this site : http://www.arndt-bruenner.de/mathe/scripts/engl_eigenwert.htm, in which some vectors are in opposing direction. Here's the example.
The matrix :
2 1 0 0
1 2 1 0
0 1 2 1
0 0 1 2

Eigenvalues : 3.16803 2.61803 1.38197 0.38197
Eigenvectors:
(my result)
0.37175  0.60150  0.60150 -0.37175
0.60150  0.37175 -0.37175  0.60150
0.60150 -0.37175  0.37175 -0.60150
0.37175 -0.60150  0.60150  0.37175
(from that website)

0.37175 -0.60150  0.60150 -0.37175
0.60150 -0.37175 -0.37175  0.60150
0.60150  0.37175  0.37175 -0.60150
0.37175  0.60150  0.60150  0.37175

Another example:
4  1 -1  2
1  4  1 -1
-1  1  4  1
2 -1  1  4

Eigenvalues : 6.00000 4.56155 5.00000 0.43845
Eigenvectors:
(my result)
0.70711  0.43516 -0.00000  0.55735
0.00000  0.55735  0.70711 -0.43516
0.00000 -0.55735  0.70711  0.43516
0.70711 -0.43516  0.00000 -0.55735

(from that website)
0.70711 -0.43516 -0.00000 -0.55735
0.00000 -0.55735  0.70711  0.43516
0.00000  0.55735  0.70711 -0.43516
0.70711  0.43516  0.00000  0.55735

(BTW, I'm going to use it in inverse kinematic) The differences are the on ones in bold. I wonder if they're the same or it's my implementation which is incorrect ? Thanks a lot.

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The opposite of an eigenvector is also an eigenvector, so I wouldn't worry [smile]

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Just to expand on Zipster....

if [p q r s]

is an eigenvector for a given eigenvalue, then any vector

[kp kq kr ks] (where k!=0)

is also an eigenvector for that same eigenvalue.

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Guys,
Thanks, so that means, it's okay if I use them in inverse kinematics, right ?

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