\begin{definition}[Definition:Non-Negative Definite Mapping]
Let $\C$ be the field of complex numbers.
Let $\F$ be a subfield of $\C$.
Let $V$ be a vector space over $\F$
Let $\left \langle {\cdot, \cdot} \right \rangle : V \times V \to \mathbb F$ be a mapping.
Then $\left \langle {\cdot, \cdot} \right \rangle : V \times V \to \mathbb F$ is '''non-negative definite''' {{iff}}:
:$\forall x \in V: \quad \left \langle {x, x} \right \rangle \in \R_{\geq 0}$
That is, the image of $\left \langle {x, x} \right \rangle$ is always a non-negative real number.
\end{definition}