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Simple Inner Product Proof (complex)

  1. Feb 28, 2013 #1
    I'm okay on proving the other properties, just struggling with what to do on this one:

    (v,v)≥0, with equality iff v=0,where the inner product is defined as:


    z1w*1+iz2w*2

    (where * represent the complex conjugate)

    My working so far is:
    u1u*1+iu2u*2
    =u1^2 + iu2^2


    (I'm not sure what to do next and how to deal with the i algebriacally. I've done real ones and complex one without an i in the definition,and seem ok with this property for them).



    Thanks alot, greatly appreaciated =].
     
  2. jcsd
  3. Feb 28, 2013 #2

    tiny-tim

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    hi binbagsss! :smile:

    (try using the X2 button just above the Reply box :wink:)
    does (u,v) = (v,u)* ? :wink:
     
  4. Feb 28, 2013 #3

    pasmith

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    Your calculations are largely correct (you need modulus signs on u1 and u2 in your final expression).

    Since [itex]\langle (u_1,u_2),(u_1,u_2)\rangle = |u_1|^2 +i|u_2|^2[/itex] is not necessarily real, the conclusion must be that [itex]\langle\cdot,\cdot\rangle[/itex] as defined is not an inner product.
     
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