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Simple Demostration

  1. Sep 18, 2004 #1
    hi, all

    Let V be a Complex Vector Space:

    probe that:

    [tex] <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 [/tex]

    Polarization formula.

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

    [tex] 4 <u\mid v> = 4 <u\mid v> - \imath 4 u [/tex]

    please help!

    thank you
     
  2. jcsd
  3. Sep 18, 2004 #2

    mathwonk

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