# Simple Demostration

1. Sep 18, 2004

### HernanV

hi, all

Let V be a Complex Vector Space:

probe that:

$$<u\mid v> = \frac {1} {4} (\parallel u + v \parallel ^ 2 - \parallel u - v \parallel ^ 2) - \frac {\imath} {4} (\parallel u + \imath v\parallel ^ 2 - \parallel u - \imath v\parallel ^ 2) \forall u,v$$

Polarization formula.

i've multiplied both sides by 4, then aplicated internal product properties and obtained...

$$4 <u\mid v> = 4 <u\mid v> - \imath 4 u$$

thank you

2. Sep 18, 2004

### mathwonk

perhaps the minus sign in front of the i/4 should be a plus sign.