       Re: Eigensystem consistency

• To: mathgroup at smc.vnet.net
• Subject: [mg84027] Re: [mg84001] Eigensystem consistency
• From: DrMajorBob <drmajorbob at bigfoot.com>
• Date: Fri, 7 Dec 2007 03:03:16 -0500 (EST)
• References: <30219775.1196952663537.JavaMail.root@m35>

```Both results ARE "the same", to the extent that equivalent eigensystems
SHOULD be the same. That is, one set of eigenvectors is just a rescaled
version of the other. The reason this can occur is that N doesn't merely
evaluate its argument, then change it to a Real. It controls evaluation of
its argument in order to get a specific precision in the result. So
Eigensystem within N computes differently.

Hence these are the same,

Eigensystem[{{\[Sigma]1^2, \[Rho] \[Sigma]1 \[Sigma]2}, {\[Rho] \
\[Sigma]1 \[Sigma]2, \[Sigma]2^2}} /.
N[{\[Sigma]1 -> 1, \[Sigma]2 -> 3, \[Rho] -> 98/100}]]
N@%

{{9.96423, 0.0357679}, {{0.311638, 0.950201}, {0.950201, -0.311638}}}

{{9.96423, 0.0357679}, {{0.311638, 0.950201}, {0.950201, -0.311638}}}

but your first expression is "different".

Bobby

On Thu, 06 Dec 2007 02:12:36 -0600, Arturas Acus <acus at itpa.lt> wrote:

> Dear group,
>
> why these two calculations give different rezults?
>
>
>
> In:= N[
>  Eigensystem[{{\[Sigma]1^2, \[Rho] \[Sigma]1 \[Sigma]2}, {\[Rho] \
> \[Sigma]1 \[Sigma]2, \[Sigma]2^2}} /. {\[Sigma]1 -> 1, \[Sigma]2 ->
>      3, \[Rho] -> 98/100}]]
>
> Out= {{9.96423, 0.0357679}, {{0.32797, 1.}, {-3.04906, 1.}}}
>
>
>
> and
>
> In:= Eigensystem[{{\[Sigma]1^2, \[Rho] \[Sigma]1 \[Sigma]2}, {\
> \[Rho] \[Sigma]1 \[Sigma]2, \[Sigma]2^2}} /.
>   N[{\[Sigma]1 -> 1, \[Sigma]2 -> 3, \[Rho] -> 98/100}]]
>
> Out= {{9.96423,
>   0.0357679}, {{0.311638, 0.950201}, {0.950201, -0.311638}}}
>
>
>
>
>
>

--

DrMajorBob at bigfoot.com

```

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