Thread: Inner Product spaces

THese spaces confuse me. I know that I have to show four axioms are satisfie but with this problem not sure how to do it.

Problem: Determine whether the function <, >:
R2 -------> R defined by < u, v > = u1^2 - v1^2 for u = (u1, u2), v = ( v1, v2) is an inner product.

Consider $\displaystyle u = \left( {1,2} \right) \quad \Rightarrow \quad \left\langle {u,u} \right\rangle = 0$.