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## Re: [Help-gsl] hi :-) \o/ I've some problem with eigensystem

 From: tuc Subject: Re: [Help-gsl] hi :-) \o/ I've some problem with eigensystem Date: Thu, 22 Apr 2010 10:20:39 +0200 User-agent: Mozilla/5.0 (X11; U; Linux x86_64; en-US; rv:1.9.1.9) Gecko/20100330 Shredder/3.0.4

hi
So the point of question is this: the
results that i get have the right values but the signs wrong.

let A be a square matrix. then a eigenvector v to the eigenvalue a is defined to have the property:
A*v=a*v.

therefor for any real number x (nonzero, zero is never an eigenvector) x*v is also a eigenvector of A:
A*(x*v)=x*(A*v)=x*(a*v)=a*(x*v)

and since (-1) is a real number, mathematically speaking both results are correct.

double data[] = { 0.616556, 0.615444,
0.615444, 0.716556};

The right results of eigen value and eigen vector:

eigenvalue= ( 0.04908339 )
( 1.28402771 )

eigenvectors = ( -0.735179  -0.677873 )
( 0.677873    -0.735179 )

The value which i took with the sample code instead are this:

eigenvalue = 0.0490843
eigenvector =
0.735179
-0.677873
eigenvalue = 1.28403
eigenvector =
0.677873
0.735179