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Subject: Re: unsorted eigenvalues
Date: Fri, 28 Sep 2007 12:49:15 +0000 (UTC)
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"Robert Sparr" <robertdotsparr@NOSPAMsri.com> wrote in
message <fdhvq6$hok$1@fred.mathworks.com>...
> I'm doing eigendecomposition-based spectral analysis, and I
> am looking for a way to recover the eigenvalues of a matrix
> (positive semidefinite Hermitian, in my case) without having
> them sorted for me.
> 
> I've seen this topic come up in other threads (such as
> "Sorted Eigenvalues & Eigenvectors?" of April 2004 and
> "non-sorting SVD" of May 2007), but the answers there
> haven't settled my problem.
> 
> In my experience, eig() always returns the eigenvalues
> sorted in ascending order, despite statements to the
> contrary in previous threads.  (Perhaps this changed with a
> recent version?)
> 
> I am aware that the eigenvectors have been sorted so that
> eigenvector index i corresponds to eigenvalue index i, and I
> know how to reconstruct the signal with the sorted output
> given by eig(), but that is not sufficient.  I also need to
> know the indexes that the significant eigenvalues had before
> they were sorted.  The ideal way to do this would be if
> eig() or some other function had an optional argument I
> could use to suppress the sorting function in eig().  (After
> all, MATLAB has an easy-to-use sort() function, if I want
> sorted output.)  Since this seems to be a recurring
> question, I suspect other people want this, too.
> 
> Thanks for any suggestions,
> R

What is the significance of unsorted eigenvalues?  I mean,
the eigenvalues are roots of the characteristic polynomial -
in what sense do these roots have order?

Best wishes, S