Polarisation

WHAT IS POLARISATION

According to the, 

  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 ${\displaystyle \|x\|}$denote the norm of vector x and ${\displaystyle \langle x,\ y\rangle }$ the inner product of vectors x and y. Then the underlying theorem, attributed 

to Fréchet, von Neumann and Jordan, is stated as:^[1][2]

In a normed space (V, ${\displaystyle \|\cdot \|}$), if the parallelogram law holds, then there is an inner product on V such that ${\displaystyle \|x\|^{2}=\langle x,\ x\rangle }$ for all ${\displaystyle x\in V}$.