polarization identity
Theorem [polarization identity] - Let be an inner product space over . The following identity holds for every :
If is an inner product space over instead, the identity becomes
Remark - This result shows that the inner product of is determined by the norm. Moreover, it can be shown that if a normed space the parallelogram law, the above formulas define an inner product compatible with the norm of .
Title | polarization identity |
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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 |