Is there a way using numpy to create a square matrix M from a smaller square matrix m?
Assuming that the shape of M is evenly divisible by shape of m (2x2):
m = [[1, 2],
[3, 4]]
array([[ 1., 2., 1., 2.],
[ 3., 4., 3., 4.],
[ 1., 2., 1., 2.],
[ 3., 4., 3., 4.]])
numpy.full((4,4), 0, dtype=numpy.int)
We can use NumPy's Kronecker product

np.kron(np.ones((2, 2), dtype=int), m)
Sample run 
In [140]: m
Out[140]:
array([[1, 2],
[3, 4]])
In [141]: np.kron(np.ones((2, 2), dtype=int), m)
Out[141]:
array([[1, 2, 1, 2],
[3, 4, 3, 4],
[1, 2, 1, 2],
[3, 4, 3, 4]])