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Re: Eigensystem[hermitianMatrix] sometimes returns

I suppose the simplest thing is





On Wed, 25 Feb 2009 03:04:51 -0600, Yen Lee Loh <yloh at>  

> Dear Mathematica users,
> In Mathematica 7.0.0 (for Linux), calling Eigenvectors[H] or  
> Eigensystem[H]
> for a numerical Hermitian matrix H sometimes returns eigenvectors that  
> are
> not orthonormal.
> This happens when some eigenvalues are degenerate.  (I can supply example
> code that illustrates the problem, if necessary.)
> This is not really a bug -- the documentation for Eigensystem[] doesn't  
> make
> any guarantees of orthonormality -- but nevertheless it is an annoying  
> part
> of Mathematica's design.
> This issue has been raised 11 years ago (
> ), but
> that post is corrupted!  (Surely Wolfram isn't resorting to  
> censorship?)  I
> was hoping that in Mathematica 7 I would be able to write something like
>     Eigensystem[H, Method->"LAPACK-ZHEEVR"]
> or
>     Eigensystem[H, OrthonormalizeEigenvectors->True]
> but no such options seem to exist.  One workaround is to apply
> Orthogonalize[] to the matrix of eigenvectors, but the documentation for
> Orthogonalize[] doesn't guarantee that the orthonormalization will only
> occur within the "degenerate subspace".  So one has to resort to  
> complicated
> fixes (e.g., ).
> Does anyone have a simpler solution?  (For example, is there an easy way  
> to
> call LAPACK'S ZHEEVR routine, which guarantees orthornormal eigenvectors,
> from Mathematica?)
> Thanks a lot.
> Yen Lee Loh

DrMajorBob at

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