Properties of a Reflection
The reflection satisfies and belongs to .
Lemma 9.13 (Properties of a Reflection)
Proof
Assume . From the formula for ,
Substituting this into the formula again gives , so is invertible with inverse . Expanding the dot product also gives
so .
Related
Stated in
- Lemma 9.13 (Properties of a Reflection)§9.3 Orthogonal Groups