Interesting fact about Hilbert spaces: The inner product of a Hilbert space induces a norm and thus every Hilbert space is a Banach space. But what about the co

Interesting fact about Hilbert spaces: The inner product of a Hilbert space induces a norm and thus every Hilbert space is a Banach space. But what about the converse? Say we only have a normed vector space, can we decide if there is an inner-product space that actually induces this norm? The answer is yes! Simply check if the Parallellogram Law [1] holds. [1] https://en.wikipedia.org/wiki/Parallelogram_law https://en.wikipedia.org/wiki/Parallelogram_law