I am reading up for my exam in Linear Algebra and found the exercise:
Let W be a finite dimensinal subspace in an inner product space $V$, and let: $$P_W : V \to W,$$ be the corresponding orthogonal projetion on W. Show that the map: $$L: V \to W^{\bot}$$ given by $$ L(v) = v-P_w(v), \ for \ v\in V $$ defines an orthogonal projection on $W^{\bot}$
I am not really sure how I am supposed to prove this, I hope someone can either show it or give me a hint towards the method.