numpy array that is (n,1) and (n,)

This is a 1D array:

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

This array is a 2D but there is only one element in the first dimension:

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

Transposing gives the shape you are asking for:

>>> np.array([[1, 2, 3]]).T.shape(3, 1)

Now, look at the array. Only the first column of this 2D array is filled.

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

Given these two arrays:

>>> a = np.array([[1, 2, 3]])>>> b = np.array([[1, 2, 3]]).T>>> aarray([[1, 2, 3]])>>> barray([[1],       [2],       [3]])

You can take advantage of broadcasting:

>>> a * barray([[1, 2, 3],       [2, 4, 6],       [3, 6, 9]])

The missing numbers are filled in. Think for rows and columns in table or spreadsheet.

>>> a + barray([[2, 3, 4],       [3, 4, 5],       [4, 5, 6]])

Doing this with higher dimensions gets tougher on your imagination.

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