\begin{definition}[Definition:Positiveness]
Let $\C$ be the field of complex numbers.
Let $\GF$ be a subfield of $\C$.
Let $V$ be a vector space over $\GF$
Let $\left \langle {\cdot, \cdot} \right \rangle : V \times V \to \GF$ be a mapping.
Then $\left \langle {\cdot, \cdot} \right \rangle : V \times V \to \GF$ is '''positive''' {{iff}}:
:$\forall x \in V: \quad \left \langle {x, x} \right \rangle = 0 \implies x = \bszero_V$
where $\bszero_V$ denotes the zero vector of $V$.
\end{definition}