RIGID Linear Transformation with NN???

[Jyh-Chian Chang]

Dear NN researcher:

   We all know that it's easy to construct a linear NN to do linear
 transformations (i.e., A = R X, here A and X are vectors and R is the
 transformation matrix). However, is it possible to build a NN to do
 RIGID linear transformations? "RIGID" means that the rotation matrix,
 R, must be an orthogonal matrix (i.e., all its columns form an
 orthonormal space; rotating without scaling and shearing).
 
   I know that there are many non-NN methods to solve this problem
 (e.g., Quaternion-based, SVD-based approaches, and so on.). Does
 anyone here have any ideas about how to build a NN to do the rigid
 linear transformations?
 
   Any suggestions are highly appreciated!  Thank you in advance!
 
 
 Garry