1. A special case of re?ection is when A is the scalar 1. Derive the algebraic outcome and interpret geometrically. Another special case is A = In; compute that and interpret. Why is the latter outcome not the dual of the former?
2. You can project onto a rotor and get a geometrically meaningful result. Give the geometric interpretation of the projection PR[x] ≡ (xJR) R -1. (Hint: Think "chord.") For rotors, it matters whether you put the inverse on the ?rst or the last factor: what is (xJR -1 ) R?