What's the name of this vector space?

Question

For a vector space $V$ and its subspace $W$, there is a vector space $W^{\perp}:= \{x\in V^{*} | \forall y\in W. x(y)=0\}$.

If $V$ is a finite dimensional inner product vector space, I think $W^\perp$ can be called orthogonal complement of $W$. However, what's the name of this in the general case?

Answer 1

That's the annihilator of $W$. It applies to any subset of $V$, not just to subspaces.