polarization identity

Theorem [polarization identityPlanetmathPlanetmath] - Let X be an inner product spaceMathworldPlanetmath over . The following identity holds for every x,yX:


If X is an inner product space over instead, the identity becomes


Remark - This result shows that the inner productMathworldPlanetmath of X is determined by the norm. Moreover, it can be shown that if a normed space V the parallelogram lawMathworldPlanetmath, the above formulas define an inner product compatible with the norm of V.

Title polarization identity
Canonical name PolarizationIdentity
Date of creation 2013-03-22 17:37:20
Last modified on 2013-03-22 17:37:20
Owner asteroid (17536)
Last modified by asteroid (17536)
Numerical id 4
Author asteroid (17536)
Entry type Theorem
Classification msc 46C05