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 :
Java
// Java code to find the Kronecker Product of// two matrices and stores it as matrix Cimport java.io.*;import java.util.*;class GFG { // rowa and cola are no of rows and columns // of matrix A // rowb and colb are no of rows and columns // of matrix B static int cola = 2, rowa = 3, colb = 3, rowb = 2; // Function to computes the Kronecker Product // of two matrices static void Kroneckerproduct(int A[][], int B[][]) { int[][] C= new int[rowa * rowb][cola * colb]; // i loops till rowa for (int i = 0; i < rowa; i++) { // k loops till rowb for (int k = 0; k < rowb; k++) { // j loops till cola for (int j = 0; j < cola; j++) { // l loops till colb for (int l = 0; l < colb; l++) { // 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]; System.out.print( C[i + l + 1][j + k + 1]+" "); } } System.out.println(); } } } // Driver program public static void main (String[] args) { int A[][] = { { 1, 2 }, { 3, 4 }, { 1, 0 } }; int B[][] = { { 0, 5, 2 }, { 6, 7, 3 } }; Kroneckerproduct(A, B); }}// This code is contributed by Gitanjali. |
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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