Python - Matrix outer product

temp = numpy.multiply.outer(A, B)
C = numpy.swapaxes(temp, 1, 2)

NumPy ufuncs, such as multiply, have an outer method that almost does what you want. The following:

temp = numpy.multiply.outer(A, B)

produces a result such that temp[a, b, c, d] == A[a, b] * B[c, d]. You want C[a, b, c, d] == A[a, c] * B[b, d]. The swapaxes call rearranges temp to put it in the order you want.

The Einstein notation expresses this problem nicely

In [85]: np.einsum('ac,bd->abcd',A,B)
Out[85]: 
array([[[[ 3,  1],
         [ 6,  2]],

        [[ 1,  2],
         [ 2,  4]]],


       [[[ 9,  3],
         [12,  4]],

        [[ 3,  6],
         [ 4,  8]]]])