Complexification of a real vector space

• November 5th 2011, 10:06 AM
dwsmith
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.
• November 5th 2011, 07:23 PM
Drexel28
Re: Complexification of a real vector space
Quote:

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 $bv$?