How to multiply rows with corresponding columns in Python (cuPy/Numpy)?

I need to multiply each row with a column at the corresponding row-index. Consider the graphics below in which I have a 3 x 3 matrix. The required operation is to multiply the row[0] of matrix with col[0] of transposed_matrix, row[1] of matrix with col[1] of transposed_matrix, and so on.

Question: How can achieve it in cupPy/Numpy Python in a smart way (i.e. without using for-loops)?

>Solution :

If you have a 3X3 array:

import numpy as np
A = np.array([[1, 2, 3],
             [4, 5, 6],
             [7, 8, 9]])

you can do:

A@A.T

but, it will produce 3X3 output

array([[ 14,  32,  50],
       [ 32,  77, 122],
       [ 50, 122, 194]])

so, if you want your desired output:

np.diag(A@A.T)

#array([ 14,  77, 194])

When the matrices are different:

B = np.array([
    [4,3,2],
    [6,9,7],
    [8,4,3]
])

np.diag(A@B.T)

#output
array([ 16, 111, 115])