Re: Eigensystem consistency
- To: mathgroup at smc.vnet.net
- Subject: [mg84012] Re: Eigensystem consistency
- From: dh <dh at metrohm.ch>
- Date: Thu, 6 Dec 2007 07:23:58 -0500 (EST)
- References: <fj8b16$au2$1@smc.vnet.net>
Hi Arturus,
I think "Eigensystem" gives unnormalized vectors if calculating with
exact numbers or symbols, but normalizes the vectors if we feed it
machine numbers. The reason may be that in the former case we may get
ungainly expressions that do not contain any additional information.
hope this helps, Daniel
Arturas Acus wrote:
> Dear group,
>
> why these two calculations give different rezults?
>
>
>
> In[1]:= 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[1]= {{9.96423, 0.0357679}, {{0.32797, 1.}, {-3.04906, 1.}}}
>
>
>
> and
>
> In[2]:= 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[2]= {{9.96423,
> 0.0357679}, {{0.311638, 0.950201}, {0.950201, -0.311638}}}
>
>
>
>
>
>