Complexification of a real vector space

**dwsmith** · November 5th 2011, 10:06 AM

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.

**Drexel28** · November 5th 2011, 07:23 PM

Originally Posted by dwsmith

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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