\begin{definition}[Definition:Outer Product]
Given two vectors $\mathbf u = \tuple {u_1, u_2, \ldots, u_m}$ and $\mathbf v = \tuple {v_1, v_2, \ldots, v_n}$, their '''outer product''' $\mathbf u \otimes \mathbf v$ is defined as:
:$\mathbf u \otimes \mathbf v = A = \begin{bmatrix}
u_1 v_1 & u_1 v_2 & \dots & u_1 v_n \\ 
u_2 v_1 & u_2 v_2 & \dots & u_2 v_n \\
 \vdots & \vdots & \ddots & \vdots \\
u_m v_1 & u_m v_2 & \dots & u_m v_n
\end{bmatrix}$
\end{definition}