Q: Problems with eigen() vs. svd()

Hi,
I have a problem understanding what is going on with eigen() for
nonsymmetric matrices.
Example:
h<-rnorm(6)

dim(h)<-c(2,3)
c<-rnorm(6)
dim(c)<-c(3,2)
Pi<-h %*% c
eigen(Pi)$values

[1] 1.56216542 0.07147773

svd(Pi)$d     

[1] 2.85537780 0.03910517

And now:

Pi2<-Pi %*% t(Pi) #that means Pi2 is symmetric and the eigenvalues should be the

# squared eigenvalues of Pi

eigen(Pi2)$values

[1] 8.153182389 0.001529214

svd(Pi2)$d     

[1] 8.153182389 0.001529214
Indeed:
diag(svd(Pi)$d) %*% diag(svd(Pi)$d)
         [,1]        [,2]
[1,] 8.153182 0.000000000
[2,] 0.000000 0.001529214

I conclude that eigen() works correctly for symmetric matrices only (or
makes sense ...).
Do I have misconceptions about the relationship between the results of
eigen()$values and
svd()$d and my conclusion is wrong ?
The VR-Book "Modern Applied Statistics" (1994) states explicitly that
eigen() is for
symmetric matrices.

Can anybody help me to clarify this point ?


Thank you

	Ralph

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