Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

Compute the Kronecker product of two multidimension NumPy arrays

  • Last Updated : 03 Sep, 2021

Given an m X n matrix A and a p X q matrix B, their Kronecker product is A ⊗ B, also called their matrix direct product, is an (m*p) X (n*q) matrix.

A = | (a00)  (a01) |
    | (a10)  (a11) |

B = | (b00)  (b01) |
    | (b10)  (b11) |

A ⊗ B = | (a00)*(b00)  (a00)*(b01)  (a01)*(b00)  (a01)*(b00) |
        | (a00)*(b01)  (a00)*(b11)  (a01)*(b01)  (a01)*(b11) | 
        | (a10)*(b00)  (a10)*(b01)  (a11)*(b00)  (a11)*(b01) |
        | (a10)*(b10)  (a10)*(b11)  (a11)*(b10)  (a11)*(b11) |

The Kronecker product of two given multi-dimensional arrays can be computed using the kron() method in the NumPy module. The kron() method takes two arrays as an argument and returns the Kronecker product of those two arrays.

 Attention geek! Strengthen your foundations with the Python Programming Foundation Course and learn the basics.  

To begin with, your interview preparations Enhance your Data Structures concepts with the Python DS Course. And to begin with your Machine Learning Journey, join the Machine Learning - Basic Level Course

Syntax:  



numpy.kron(array1, array2)

Below are some programs which depict the implementation of kron() method in computing Kronecker product of two arrays:

Example 1:  

Python3




# Importing required modules
import numpy
 
# Creating arrays
array1 = numpy.array([[1, 2], [3, 4]])
print('Array1:\n', array1)
 
array2 = numpy.array([[5, 6], [7, 8]])
print('\nArray2:\n', array2)
 
# Computing the Kronecker Product
kroneckerProduct = numpy.kron(array1, array2)
print('\nArray1 ⊗ Array2:')
print(kroneckerProduct)

Output: 

Array1:
 [[1 2]
 [3 4]]

Array2:
 [[5 6]
 [7 8]]

Array1 ⊗ Array2:
[[ 5  6 10 12]
 [ 7  8 14 16]
 [15 18 20 24]
 [21 24 28 32]]

Example 2: 

Python3




# Importing required modules
import numpy
 
# Creating arrays
array1 = numpy.array([[1, 2, 3]])
print('Array1:\n', array1)
 
array2 = numpy.array([[3, 2, 1]])
print('\nArray2:\n', array2)
 
# Computing the Kronecker Product
kroneckerProduct = numpy.kron(array1, array2)
print('\nArray1 ⊗ Array2:')
print(kroneckerProduct)

Output: 

Array1:
 [[1 2 3]]

Array2:
 [[3 2 1]]

Array1 ⊗ Array2:
[[3 2 1 6 4 2 9 6 3]]

Example 3: 

Python3




# Importing required modules
import numpy
 
# Creating arrays
array1 = numpy.array([[1, 2, 3], [4, 5, 6]])
print('Array1:\n', array1)
 
array2 = numpy.array([[1, 2], [3, 4], [5, 6]])
print('\nArray2:\n', array2)
 
# Computing the Kronecker Product
kroneckerProduct = numpy.kron(array1, array2)
print('\nArray1 ⊗ Array2:')
print(kroneckerProduct)

Output: 

Array1:
 [[1 2 3]
 [4 5 6]]

Array2:
 [[1 2]
 [3 4]
 [5 6]]

Array1 ⊗ Array2:
[[ 1  2  2  4  3  6]
 [ 3  4  6  8  9 12]
 [ 5  6 10 12 15 18]
 [ 4  8  5 10  6 12]

 




My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!