In this chapter, we will discuss the Multiplication and Dot Product of two NumPy arrays.
Multiplication
Multiplication between two NumPy arrays is an element-wise product, and is represented by '*'
e.g.
import numpy as np
A = np.array( [ [ 1,1], [0, 1] ] )
B = np.array( [ [2, 0], [3, 4] ] )
Please note, this element-wise product '*' is different from 'dot product '.' of matrices.
'dot product' is also known as 'matrix product'.
M = A * B
print(A)
array([ [1, 1],
[0, 1] ])
print(B)
array( [ [2, 0],
[3, 4] ] )
print(M)
Output (M) will be
array([ [2, 0 ],
[0, 4] ] )
Above, element-wise product(M) is computed as below
M = [ [ A[1, 1] * B[1, 1], A[1, 2] * B[1, 2] ],
[ A[2, 1] * B[2, 1], A[2, 2] * B[2, 2] ] ]
= [ [ (1 * 2), (1 * 0)],
[ (0 * 3), (1, 4) ] ]
M = [ [2, 0],
[0, 4] ]
Matrix Product (or Dot Product)
Matrix Product (or Dot Product) between two NumPy is different from the element-wise product (or Multiplication). The dot product is represented by '.'
e.g.
import numpy as np
C = np.array( [ [ 1,1], [0, 1] ] )
D = np.array( [ [2, 0], [3, 4] ] )
Please note, this dot product '.' or 'matrix product' is different from 'element-wise' product '*'
P = np.dot(C, D)
print(C)
array([ [1, 1],
[0, 1] ])
print(D)
array( [ [2, 0],
[3, 4] ] )
print(P)
Output (P) will be
array([ [5, 4 ],
[ 3, 4] ] )
Above, element-wise product(P) is computed as below
P = [ [ [( (C[1,1] * D[1, 1]) + (C[1, 2] * D[2, 1] ) )], [( (C[1,1] * D[1, 2]) + (C[1, 2] * D[2, 2] ) )] ],
[ [( (C[2,1] * D[1, 1]) + (C[2, 2] * D[2, 1] ) )], [( (C[2,1] * D[1, 2]) + (C[2, 2] * D[2, 2] ) )] ] ]
= [ [ ( (1 * 2) + (1 * 3) ), ( (1 * 0) + (1 * 4) ) ],
[ ( (0 * 2) + (1 * 3) ), ( (0 * 2) + (1 * 4) ) ] ]
= [ [ (2 + 3), (0 + 4) ],
[ (0 + 3), (0 + 4) ] ]
= [ [5, 4],
[3, 4] ]
Please follow the below steps:
(1) Please import required libraries
import numpy as np
Multiplication (element-wise product)
(2) Create two NumPy arrays - A_arr and B_arr - as shown below
A_arr = np.array([ [ 5,9], [4, 7] ])
B_arr = np.array( [ [2, 8], [1, 6] ] )
(3) Multiply the above two NumPy arrays (A_arr and B_arr) and store the result in a variable M_arr
<<your code comes here>> = A_arr << your code comes here>> B_arr
(4) Print the array M_arr to see its values
print(<<your code comes here>>)
Dot Product (Matrix Product)
(1) Create two NumPy arrays - C_arr and D_arr - as shown below
C_arr = np.array([ [ 5,9], [4, 7] ])
D_arr = np.array( [ [2, 8], [1, 6] ] )
(2) Perform dot product of the above two NumPy arrays (C_arr and D_arr) and store the result in a variable P_arr
<<your code comes here>> = np.dot(<<your code comes here>>)
(3) Print the array P_arr to see its values
print(<<your code comes here>>)
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