Definition:Semi-Inner Product Space/Real Field

Definition
Let $\R$ be the real numbers.

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 semi-inner product on $V$.

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

That is, a (real) semi-inner product space is a vector space over a subfield of the real numbers together with an associated real semi-inner product.

Also see

 * Definition:Inner Product


 * Definition:Inner Product Space


 * User:Leigh.Samphier/Refactor/Real Semi-Inner Product Space is Complex Semi-Inner Product Space