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From: "Bruno Luong" <b.luong@fogale.findmycountry>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Eigenvectors with Identical Eigenvalues Lose orthogonality?
Date: Fri, 6 Aug 2010 17:37:04 +0000 (UTC)
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"NIcholas " <dsfadfa@aol.com> wrote in message <i3hcrc$g9o$1@fred.mathworks.com>...
> Shouldn't the command "[V,D] = eig(A);" give an orthogonal basis V?
> If A has unique eigenvalues I find this to be true, but if A has identical eigenvalues (see code below) the eigenvectors with identical eigenvalues seem to lose orthogonality.  Is this a numerical issue with the eig command? and is there a way around it?

This is not an "issue": there is no warranty that EIG must return the orthogonal basis for multiple-order eigenspace even for Hermitian matrix. Any basis vectors within the multilple-order eigenspace are still *valid* eigen-vectors.

If you want to reorthonalize, use ORTH after EIG. Or you can call SVD

[V D V] = svd(A)

Bruno