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 
$$A = \begin{pmatrix}1 & 2 \\ 3 & 4\end{pmatrix} \qquad B = \begin{pmatrix}5 & 6 & 7 \\ 8 & 9 & 10\end{pmatrix}$$
 A: The outer product usually refers to the tensor product of vectors.
If you want something like the outer product between a $m \times n$ matrix $A$ and a $p\times q$ matrix $B$, you can see the generalization of outer product, which is the Kronecker product. It is noted $A \otimes B$ and equals:
$$A \otimes B = \begin{pmatrix}a_{11}B & \dots & a_{1n}B \\ \vdots & \ddots &  \vdots \\ a_{m1}B & \dots & a_{mn}B\end{pmatrix}$$
A: To extend davcha's answer, for your specific example, you would get:
$$A\otimes B=
\left(
\begin{array}{cc}
 \left(
\begin{array}{ccc}
 5 & 6 & 7 \\
 8 & 9 & 10 \\
\end{array}
\right) & \left(
\begin{array}{ccc}
 10 & 12 & 14 \\
 16 & 18 & 20 \\
\end{array}
\right) \\
 \left(
\begin{array}{ccc}
 15 & 18 & 21 \\
 24 & 27 & 30 \\
\end{array}
\right) & \left(
\begin{array}{ccc}
 20 & 24 & 28 \\
 32 & 36 & 40 \\
\end{array}
\right) \\
\end{array}
\right)
$$
A: I think @davcha and @Sandu Ursu 's answers are wrong. They have calculated the Kronecker Product.
According to the definition of outer product,  the outer product of A and B should be a $2×2×2×3$ tensor. You can follow this answer to compute it using numpy.
