R help - Jul 2004 - Any orthnormal matrix can keep the curve's shape and size unchnaged?

Dear R users,
 
I want to know, given a curve f in d-dimensional space, 
It is possible to keep the curve’s shape and size unchanged by
an arbitrary dxd orthnormal matrix A?
That is, the new curve g = A*f is still the same shape and size as f?
 
Thanks for your advices and answers.
 
 
Fred

	[[alternative HTML version deleted]]

Any orthogonal transformation preserves angles between vectors and
their length. Therefore, I guess shape and size are preserved -- of
course a precise answer depends on how you define these two features
of a curve. 

I am missing what has all this to do with R, though.

Giovanni
> Date: Thu, 29 Jul 2004 15:08:52 -0500
> From: Fred <fzh113 at hecky.it.northwestern.edu>
> Sender: r-help-bounces at stat.math.ethz.ch
> Cc: 
> Importance: Normal
> Precedence: list
> 
> Dear R users,
>  
> I want to know, given a curve f in d-dimensional space, 
> It is possible to keep the curve?s shape and size unchanged by
> an arbitrary dxd orthnormal matrix A?
> That is, the new curve g = A*f is still the same shape and size as f?
>  
> Thanks for your advices and answers.
>  
>  
> Fred
> 
> 	[[alternative HTML version deleted]]
> 
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> 
> 
-- 

 __________________________________________________
[                                                  ]
[ Giovanni Petris                 GPetris at uark.edu ]
[ Department of Mathematical Sciences              ]
[ University of Arkansas - Fayetteville, AR 72701  ]
[ Ph: (479) 575-6324, 575-8630 (fax)               ]
[ http://definetti.uark.edu/~gpetris/              ]
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