Let V be an inner product space and W a finite-dimensional subspace of V. There are (in general) many projections which have W as their range. One of these, the orthogonal projection on W, has the property that ∥Eα∥≤∥α∥ for every α in V. Prove that if E is a projection with range W, such that ∥Eα∥≤∥α∥ for all α in V, then E is the orthogonal projection on W.