[R] Any orthnormal matrix can keep the curve's shape and size unchnaged?

[Spencer Graves]

  How do you define "size and shape"? The answer is probably yes. 
However, if you have an essentially 2-d circle embedded in a 3-d space, 
and "size and shape" are defined in terms of a 2-d projection, this 
circle could be rotated into an ellipse in any orientation and even to a 
line.

Also, if f is an N x d dimensional matrix approximating your object and 
A is a d x d orthogonal matrix, then I think your transformation in R 
would be written "f %*% A".

hope this helps. spencer graves

Giovanni Petris wrote:

>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
>
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>>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
>>
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