# Thread: Complexification of a real vector space

1. ## Complexification of a real vector space

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

Haven't a clue how to work this one.

2. ## Re: Complexification of a real vector space

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

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 $\displaystyle (a+bi)v$ to $\displaystyle av$ and $\displaystyle bv$?