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}}}

>

>

>

>

>

>

```

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