4. Let n E IN and fix p, q E R". Define the linear map L: R" -> R" by L(x) = (x . p)q, where we use the dot-product. You do not need to prove that L is indeed linear. What is the adjoint L* of L? Proposition 7.13. Let R" be equipped with the Euclidean inner product. Let L: R" - Rn be a linear transformation. Then there exists a unique linear map L* : R" -> R", called the adjoint of L, such that (Lx, y) = (x, L'y) for all x, y E Rn