Numpy transpose weird output

So you have two arrays: np.array([3, 2, 3]).T (which is identical to the non-tranposed version: np.array([3, 2, 3])), and np.array([[3],[2],[1]]). Let's look at each one:

>>> a = np.array([3, 2, 3])
>>> a
array([3, 2, 3])

>>> b = np.array([[3],[2],[1]])
>>> b
array([[3],
       [2],
       [1]])

Note how the first (a) is 1D, while the second (b) is 2D. Since they have different dimensions, trying to compare them will do what's called "numpy broadcasting", and it's a really cool feature.

To break it down:

>>> a == b
array([[ True, False,  True],
       [False,  True, False],
       [False, False, False]])

Basically what the does, is for every item E in b, it checks if all the items in a are equal to E. To prove that:

>>> a == b[0]
array([ True, False,  True])

>>> a == b[1]
array([False,  True, False])

>>> a == b[2]
array([False, False, False])

Notice how the above arrays are identical to the whole array made by a == b. That's because a == b is a short, efficient form of doing the above.