now y is in W, x-p is orthogonal to W so
Let x ∈ Rn and let p be the orthogonal projection of x onto W where W is a subspace of Rn. Provethat for all y ∈ W ,
||x−(p+y)||2 =||x−p||2 +||y||2.
Now expanding out using the defn of norm (dot product) doesn't get me very far, any hints?