R help - Mar 2010 - Howto get unnormalized eigenvectors?

Hi,
I try to calculate the angle between two first eigenvectors of different
covariance matrices of biological phenotypic traits for different populations.
My issue here is, that all possibilities to do so seem to normalize the
eigenvectors to length 1. Although the helpfile of eigen() states, that using
eigen(, symmetric = FALSE, EISPACK =TRUE) skips normalization this is (I guess)
not applicable for me as my matrices are symmetric.

x<-eigen(cov(population1))$vectors[,1]
y<-eigen(cov(population2))$vectors[,1]

angle (in degree):
((acos((x%*%y)/(sqrt(x%*%y)*sqrt(y%*%y))))*180)/pi
Thus by using normalized vectors, the divisor becomes meaningless being 1.

Does anybody have an idea to get raw eigenvectors?
Thanks a lot

Kay Lucek
Aquatic Ecology & Macroevolution
University of Bern
Baltzerstr. 6
3012 Bern
Switzerland

Lucek, Kay wrote:
> Hi,
> I try to calculate the angle between two first eigenvectors of different
covariance matrices of biological phenotypic traits for different populations.
My issue here is, that all possibilities to do so seem to normalize the
eigenvectors to length 1. Although the helpfile of eigen() states, that using
eigen(, symmetric = FALSE, EISPACK =TRUE) skips normalization this is (I guess)
not applicable for me as my matrices are symmetric.
>
> x<-eigen(cov(population1))$vectors[,1]
> y<-eigen(cov(population2))$vectors[,1]
>
> angle (in degree):
> ((acos((x%*%y)/(sqrt(x%*%y)*sqrt(y%*%y))))*180)/pi
> Thus by using normalized vectors, the divisor becomes meaningless being 1.
>
> Does anybody have an idea to get raw eigenvectors?
I don't know what you mean by "raw eigenvectors".  Any non-zero
multiple
of an eigenvector is an eigenvector.

For the angle, just skip the denominator, because it's guaranteed to be 1.

Duncan Murdoch