# What is a proper rotation?

1. Nov 7, 2014

2. Nov 7, 2014

### Meir Achuz

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

3. Nov 7, 2014

### 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."