+\subsection{Dual space}
+
+\subsection{Inner and outer product}
+\label{math_app:product}
+
+\begin{definition}
+The inner product ...
+\end{definition}
+
+\begin{definition}
+If $\vec{u}\in U$ and $\vec{v}\in V$ are vectors within the respective vector spaces and $V^{\dagger}$ is the dual space of $V$, the outer product of $\vec{u}$ and $\vec{v}$ is defined as the tensor product ...
+\end{definition}
+