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, $$\begin{equation} \mathbf{A}= \mathbf{yz}^T \Longrightarrow a_{ij} = y_{i}z_{j}, \tag{10} \end{equation}$$

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