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orthonormal eigenvectors

• To: mathgroup at smc.vnet.net
• Subject: [mg67576] orthonormal eigenvectors
• From: tkg <tkghosh at mp.okayama-u.ac.jp>
• Date: Sat, 1 Jul 2006 05:12:05 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

Hi, I am trying to calculate eigenvalues and the corresponding ORTHONORMAL eigenvectors of a square, real, and hermitian matrix (10 X 10 matrix). I use either Eigenvalues & Eigenvectors or Eigensystem. It gives me real, distinct eigenvalues and the corresponding eigenvectors. These eigenvectors are normalized but not orthogonal to each other. Then I use GramSchmidt method to make them orthogonal. It makes them orthogonal, but these new orthogonal eigenvectors are not consistent with the eigenvalues!
Do you have any idea how to sort out this problem? 
I mean, is there any way to get eigenvalues with the corresponding ORTHONORMAL eigenvectors?

Thank you in advance.

• Follow-Ups:
  • Re: orthonormal eigenvectors
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>