Proving that a function is not an inner product

Question

I have this function here that I need to prove is not an inner product.

I've been able to use the first three axioms (symmetry, additivity and homogeneity), which the function has satisfied, but I'm not sure how to go about using the positivity axiom to prove that it is not an inner product space.

How would I go about doing this?

Answer 1

Let $v=(0,0,1,0)$ and compute $\langle v,v\rangle.$