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Math Help - imagine and real part of inner product?

  1. #1
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    imagine and real part of inner product?

    http://i37.tinypic.com/118j0p1.jpg

    uppon what law this transition was made?
    how did they deside what is the real and what is the imaginate part?
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  2. #2
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    The "decide" what are the real and imaginary parts of a number from the definition: If x= a+ bi then the real part of x is a and the imaginary part is b.

    They are also using the "linearity" of the inner product,
    <au+ bv, w>= a<u, w>+ b<v, w>. and the fact that <u, v>= \overline{<u, v>} so that <u, av+ bw>= \overline<av+ bw, u>= \overline{a<v,u>}+ \overline{b<w,u>} = \overline{a}<u, v>+ \overline{b}<u, w>.
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  3. #3
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    thanks
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