How to subtract a column value with every value in another column (pandas)

Question

I have two columns A and B. I want to subtract column B value with every value in column A and create a new column without using for-loop.

Below is my Dataframe

    A   B
0   5   3
1   3   2
2   8   1

Desired output

    A   B   C   D   E
0   5   3   2   3   4   
1   3   2   0   1   2
2   8   1   5   6   7

C = A - B[0]
D = A - B[1]
E = A - B[2]

Answer 1

Using numpy's array broadcasting:

df = pd.DataFrame({'A':[5, 3, 8],
                   'B':[3, 2, 1]})

df2 = pd.DataFrame(df['A'].values[:, None] - df['B'].values, columns=['C', 'D', 'E'])

df = df.join(df2)

Result:

   A  B  C  D  E
0  5  3  2  3  4
1  3  2  0  1  2
2  8  1  5  6  7

Explanation:

>>> df['A'].values[:, None]

array([[5],
       [3],
       [8]])

>>> df['B'].values

array([3, 2, 1])

When subtracting them, numpy "stretches" df['A'].values[:, None] to:

array([[5, 5, 5],
       [3, 3, 3],
       [8, 8, 8]])

and df['B'].values to:

array([[3, 2, 1],
       [3, 2, 1],
       [3, 2, 1]])

and the result of subtraction is:

array([[2, 3, 4],
       [0, 1, 2],
       [5, 6, 7]])