Q: Problems with eigen() vs. svd() - R-help

ralle

Wed, May 10, 2000 4:37 AM #

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

[1] 1.56216542 0.07147773

[1] 2.85537780 0.03910517

And now:

# squared eigenvalues of Pi

[1] 8.153182389 0.001529214

[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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Brian Ripley

Wed, May 10, 2000 4:44 AM #

On Wed, 10 May 2000, ralle wrote:

It does not on any of the pages indexed under `eigen', and on those pages
it "explicitly" discusses simplifications if the matrix is symmetric and
the `symmetric' argument!

Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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Paul Gilbert

Wed, May 10, 2000 6:28 AM #

As I recall, eigen() in Splus did only work for symmetric matrices sometime in
the last millenium. I believe it changed around 1994. I don't think R had
eigen() until around 1996, and I believe it may not have worked with
non-symmetric matrices at first, but that changed very quickly. History buffs
please correct me. I work with time series but I'm not good at remembering
dates.

Paul Gilbert

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