Polarization Identity

In mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space. Let denote the norm of vector x and the inner product of vectors x and y. Then the underlying theorem, attributed to Fréchet, von Neumann and Jordan, is stated as:

In a normed space (V, ), if the parallelogram law holds, then there is an inner product on V such that for all .