Definition:Inner Product Space/Real Field

Definition
Let $\GF$ be a subfield of $\R$.

Let $V$ be a vector space over $\GF$.

Let $\innerprod \cdot \cdot : V \times V \to \GF$ be an real inner product on $V$.

We say that $\struct {V, \innerprod \cdot \cdot}$ is a (real) inner product space.

That is, an (real) inner product space is a real vector space together with an associated real inner product.

Also see

 * Definition:Inner Product


 * Definition:Semi-Inner Product Space
 * Definition:Hilbert Space