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Finding the inner product given the norm [duplicate]

Possible Duplicate: Norms Induced by Inner Products and the Parallelogram Law So suppose we are given a norm on a vector space. If the Parallelogram law holds does that automatically mean we ...
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From norm to scalar product

In the Eculidean Space, one can automatically define a norm if a specific scalar product is given. On the contrary, it's not always true. A p-norm is a scalar product if and only if p=2. My question ...
It is known that the parallelogram law $\|x-y\|^2+\|x+y\|^2 = 2(\|x\|^2 + \|y\|^2)$ holds in any space with an inner product (the norm being induced by this inner product). Is this formula valid in ...