Outer Product of Two Matrices? How would I go about calculating the outer product of two matrices of 2 dimensions each?  From what I can find, outer product seems to be the product of two vectors, $u$ and the transpose of another vector, $v^T$.  
As an example, how would I calculate the outer product of $A$ and $B$, where 
$$A = \begin{pmatrix}1 & 2 \\ 3 & 4\end{pmatrix} \qquad B = \begin{pmatrix}5 & 6 & 7 \\ 8 & 9 & 10\end{pmatrix}$$

To extend davcha's answer, for your specific example, you would get:
$$A\otimes B=
\left(
\begin{array}{cc}
 \left(
\begin{array}{ccc}
 5 & 6 & 7 \\
 8 & 9 & 10 \\
\end{array}
\right) & \left(
\begin{array}{ccc}
 10 & 12 & 14 \\
 16 & 18 & 20 \\
\end{array}
\right) \\
 \left(
\begin{array}{ccc}
 15 & 18 & 21 \\
 24 & 27 & 30 \\
\end{array}
\right) & \left(
\begin{array}{ccc}
 20 & 24 & 28 \\
 32 & 36 & 40 \\
\end{array}
\right) \\
\end{array}
\right)
$$
