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MathGroup Archive 2003

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orthonormalized eigenvectors

  • To: mathgroup at smc.vnet.net
  • Subject: [mg44450] orthonormalized eigenvectors
  • From: Mahn-Soo Choi <mahn-soo.choi at unibas.ch>
  • Date: Mon, 10 Nov 2003 04:52:20 -0500 (EST)
  • Organization: Korea University
  • Sender: owner-wri-mathgroup at wolfram.com

As far as I see, the eigenvectors returned from Eigenvectors[] or
Eigensystems[] are not orthogonal for *Hermitian matrices with
degenerate eigenvalues*.  (For non-degenate Hermitian matrices, of
course, the eigenvectors are orthogonal as they should be.)

Even worse is when the eigenvalues of a Hermitian matrix are nearly
degenerate.

Of course, I could use the singular value decomposition to
orthonormalize the eigenvectors.  But then I need to evaluate the
eigenvectors again to get proper correspondence between the eigenvectors
and eigenvalues.

This is very frustrating to me because I have to calculate eigenvalues
and corresponding *orthonormalized* eigenvectors numerically for quite
big Hermitian matrices.

Is there any effecient method working with Mathematica to calculate
numerically the eigenvalues and corresponding *orthonormalized*
eigenvectors for Hermitian matrices with possibly *degenerate*
eigenvalues?

Many thanks in advance for your help.

Best,

mahn-soo




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