Java Program for Kronecker Product of two matrices

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Given a ${m} imes{n}$ matrix A and a ${p} imes{q}$ matrix B, their Kronecker product C = A tensor B, also called their matrix direct product, is an ${(mp)} imes{(nq)}$ 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 C
import 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!