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Re: eigenvector rotation

• To: mathgroup at smc.vnet.net
• Subject: [mg46673] Re: eigenvector rotation
• From: "Steve Luttrell" <steve1 at _removemefirst_luttrell.org.uk>
• Date: Fri, 27 Feb 2004 19:32:01 -0500 (EST)
• References: <c1luu7$o16$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

If you multiply all of the eigenvectors of a Hermitian matrix H by Exp[I
theta] where theta is real then you still have a valid set of eigenvectors
(i.e. they satisfy the H xi = lambdai xi, and the orthonormality conditions
<xi|xj> = KroneckerDelta[i,j] are satisfied). That means that the value of
theta is arbitrary so Mathematica can use any theta she wants, and you can
then multiply Mathematica's result by your own Exp[I theta].

Steve Luttrell

"Bettina" <bho at em.uni-karlsruhe.de> wrote in message
news:c1luu7$o16$1 at smc.vnet.net...
> Hi
> It seems, that when I calculate the eigensystem of a complex Hermitian
> matrix, th eigenvectors get rotated automatically in such a way, that
> the highest absolute valued eigenvector component becomes real. Since I
> need the unrotated result, how do I switch off this feature?
> Thanks for the help.
> Best regards
> Bettina
>