Difference between np.dot and np.multiply with np.sum in binary cross-entropy loss calculation

Question

I have tried the following code but didn\'t find the difference between np.dot and np.multiply with np.sum

Here is np.dot

Answer 1

np.dot is the dot product of two matrices.

|A B| . |E F| = |A*E+B*G A*F+B*H|
|C D|   |G H|   |C*E+D*G C*F+D*H|

Whereas np.multiply does an element-wise multiplication of two matrices.

|A B| ⊙ |E F| = |A*E B*F|
|C D|   |G H|   |C*G D*H|

When used with np.sum, the result being equal is merely a coincidence.

>>> np.dot([[1,2], [3,4]], [[1,2], [2,3]])
array([[ 5,  8],
       [11, 18]])
>>> np.multiply([[1,2], [3,4]], [[1,2], [2,3]])
array([[ 1,  4],
       [ 6, 12]])

>>> np.sum(np.dot([[1,2], [3,4]], [[1,2], [2,3]]))
42
>>> np.sum(np.multiply([[1,2], [3,4]], [[1,2], [2,3]]))
23