Important Mathematical Operations
$$
\begin{equation}
\mathbf{x}=\mathbf{yz} \Longrightarrow x_{i} = y_{i}z_i,
\tag{8}
\end{equation}
$$
the inner or so-called dot product resulting in a constant
$$
\begin{equation}
x=\mathbf{y}^T\mathbf{z} \Longrightarrow x = \sum_{j=1}^{n} y_{j}z_{j},
\tag{9}
\end{equation}
$$
and the outer product, which yields a matrix,
$$
\begin{equation}
\mathbf{A}= \mathbf{yz}^T \Longrightarrow a_{ij} = y_{i}z_{j},
\tag{10}
\end{equation}
$$