Given a 
matrix A and a 
matrix B, their Kronecker product C = A tensor B, also called their matrix direct product, is an 
matrix.
A tensor B = |a11B a12B|
|a21B a22B|
= |a11b11 a11b12 a12b11 a12b12|
|a11b21 a11b22 a12b21 a12b22|
|a11b31 a11b32 a12b31 a12b32|
|a21b11 a21b12 a22b11 a22b12|
|a21b21 a21b22 a22b21 a22b22|
|a21b31 a21b32 a22b31 a22b32|
Examples:
1. The matrix direct(kronecker) product of the 2×2 matrix A
and the 2×2 matrix B is given by the 4×4 matrix :
Input : A = 1 2 B = 0 5
3 4 6 7
Output : C = 0 5 0 10
6 7 12 14
0 15 0 20
18 21 24 28
2. The matrix direct(kronecker) product of the 2×3 matrix A
and the 3×2 matrix B is given by the 6×6 matrix :
Input : A = 1 2 B = 0 5 2
3 4 6 7 3
1 0
Output : C = 0 5 2 0 10 4
6 7 3 12 14 6
0 15 6 0 20 8
18 21 9 24 28 12
0 5 2 0 0 0
6 7 3 0 0 0
Below is the code to find the Kronecker Product of two matrices and stores it as matrix C :
Python3
# Python3 code to find the Kronecker Product of two# matrices and stores it as matrix C # rowa and cola are no of rows and columns# of matrix A# rowb and colb are no of rows and columns# of matrix Bcola = 2rowa = 3colb = 3rowb = 2 # Function to computes the Kronecker Product# of two matricesdef Kroneckerproduct( A , B ): C = [[0 for j in range(cola * colb)] for i in range(rowa * rowb)] # i loops till rowa for i in range(0, rowa): # k loops till rowb for k in range(0, rowb): # j loops till cola for j in range(0, cola): # l loops till colb for l in range(0, colb): # Each element of matrix A is # multiplied by whole Matrix B # resp and stored as Matrix C C[i + l + 1][j + k + 1] = A[i][j] * B[k][l] print (C[i + l + 1][j + k + 1],end=' ') print ("") # Driver code.A = [[0 for j in range(2)] for i in range(3)]B = [[0 for j in range(3)] for i in range(2)]A[0][0] = 1A[0][1] = 2A[1][0] = 3A[1][1] = 4A[2][0] = 1A[2][1] = 0B[0][0] = 0B[0][1] = 5B[0][2] = 2B[1][0] = 6B[1][1] = 7B[1][2] = 3Kroneckerproduct( A , B )# This code is contributed by Saloni. |
Output :
0 5 2 0 10 4 6 7 3 12 14 6 0 15 6 0 20 8 18 21 9 24 28 12 0 5 2 0 0 0 6 7 3 0 0 0
Time Complexity: O(rowa*rowb*cola*colb), as we are using nested loops.
Auxiliary Space: O((rowa + colb) * (rowb + cola)), as we are not using any extra space.
Please refer complete article on Kronecker Product of two matrices for more details!
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