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Math Help - Inner product space

  1. #1
    Senior Member vincisonfire's Avatar
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    Inner product space

    Show that if V = \mathbb C^n
    , then for any inner product on V , there
    is a unique complex n n matrix A such that  \langle \vec{v},\vec{w}\rangle =\vec{v}^T A \overline{\vec{w}} for
    all  \ \vec{v},\vec{w}\in V.
    How to show existence?
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  2. #2
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    What happens to the usual basis vectors, i.e. <e_i,e_j> where e_i is the vector with 1 in the ith coordinate and 0 elsewhere? Note that, assuming such a representation is always possible, <e_i,e_j>=a_{ij}.
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