What is an example of a proper rotation in physics?

[Sicktoaster]

An example being its use in the beginning of this document:

http://isites.harvard.edu/fs/docs/icb.topic1288789.files/Rotations-Lorentz-Transformations.pdf

I haven't read the whole document yet so forgive me if it explains what it means later on.

 

[Meir Achuz]

'proper' usually means the determinant of the transformation matrix is +1.

 

[Dr.D]

Meir Achuz comment is correct, as far as it goes. If the determinant is +1, a right-handed coordinate system is transformed into a right-handed coordinate system; this is a "proper" (or physically realizable) transformation.

If the determinant is -1, the transformation is "improper" which is to say that a right-handed system is transformed into a left-handed system, and vice versa. This is improper in that it cannot be realized physically because "it turns space inside out."