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