You can do something like this:
>>> import numpy as np
>>> from itertools import combinations
>>> A = np.array([[1, 2, 3], [4, 5, 6], [10, 20, 30]])
>>> [np.linalg.norm(a-b) for a, b in combinations(A, 2)]
[5.196152422706632, 33.674916480965472, 28.930952282978865]