Φv,w(x) := ⟨v,x⟩ * w - ⟨w,x⟩ *v
Gesetze über Skalarprodukt anwenden:
⟨Φv,w(x),y⟩
= ⟨ ⟨v,x⟩ * w - ⟨w,x⟩ *v , y ⟩
= ⟨ ⟨v,x⟩ * w ,y ⟩ - ⟨ ⟨ w,x⟩ *v , y ⟩
= ⟨v,x⟩ * ⟨w ,y ⟩ - ⟨ w,x⟩ * ⟨ v , y ⟩
= ⟨w,y⟩ * ⟨x, v ⟩ - ⟨v,y⟩ * ⟨x,w ⟩
= ⟨x, ⟨w,y⟩ * v ⟩ - ⟨x, ⟨v,y⟩ *w ⟩
= ⟨x, ⟨w,y⟩ * v - ⟨v,y⟩ *w ⟩
= ⟨x,Φw,v(y)⟩