\begin{definition}[Definition:Conjugate Symmetric 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 $\innerprod \cdot \cdot: V \times V \to \mathbb F$ be a mapping.
Then $\innerprod \cdot \cdot: V \times V \to \mathbb F$ is '''conjugate symmetric''' {{iff}}:
:$\forall x, y \in V: \quad \innerprod x y = \overline {\innerprod y x}$
where $\overline {\innerprod y x}$ denotes the complex conjugate of $\innerprod x y$.
\end{definition}