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Math Help - Complexification of a real vector space

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    Complexification of a real vector space

    Let V be a complex vector space, with conjugation \chi:V\to V. Prove that a subspace W of V is the complexification of a real vector space S iff W is close under \chi

    Haven't a clue how to work this one.
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    MHF Contributor Drexel28's Avatar
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    Re: Complexification of a real vector space

    Quote Originally Posted by dwsmith View Post
    Let V be a complex vector space, with conjugation \chi:V\to V. Prove that a subspace W of V is the complexification of a real vector space S iff W is close under \chi

    Haven't a clue how to work this one.
    It's closed under everything except for possibly the multiplication by complex scalars. Now, how precisely do we define (a+bi)v to av and bv?
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