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orthonormal version of Eigensystem[]?

Dear Mathematica users

I admire the version of Eigensystem[] on Mathematica very much.  It is
fast and accurate, even for the 1000 x 1000 symmetric real matrices
than I am looking at.

But Eigensystem[] has one very important limitation when solving a
symmetric real matrix, or more generally when solving a complex
Hermitian matrix.  This limitation is poorly documented and can "bite"
the unwary user, as I found from personal experience.

Namely, although Eigensystem[] usually returns a set of orthonormal
eigenvectors when given a real symmetric matrix, it is not *guaranteed*
do so.  Specifically in the case where two eigenvalues are degenerate,
the returned eigenvectors are (occasionally but not always) grossly

Now, this behavior is perfectly consistent with the documentation of
Eigensystem[], which is completely silent on the issue of eigenvector
orthonormality.  The reason the behavior is aFrom Sun Mar 22 03:23:15 1998
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From: (Dimiter Petsev)
Subject: [mg11657] diffusion equation in two dimensions

Dear Colleagues, 

I am trying to solve a two dimensional diffusion equation with a
coordiante  dependent diffusion tensor.  Therefore, I wonder if there
is any Mathematica  package available which might be of any help.  

Any advise sent to will be greatly


Dimiter Petsev

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