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Kronecker Product of two matrices

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  • Difficulty Level : Easy
  • Last Updated : 02 Dec, 2022
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Given an m*n matrix A and a p*q matrix B, their Kronecker product C = A tensor B, also called their matrix direct product, is a (m*p) * (n*q) 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    
Recommended Practice

Below is the code to find the Kronecker Product of two matrices and stores it as matrix C : 

C++




// C++ code to find the Kronecker Product of two
// matrices and stores it as matrix C
#include <bits/stdc++.h>
using namespace std;
 
// rowa and cola are no of rows and columns
// of matrix A
// rowb and colb are no of rows and columns
// of matrix B
const int cola = 2, rowa = 3, colb = 3, rowb = 2;
 
// Function to computes the Kronecker Product
// of two matrices
void Kroneckerproduct(int A[][cola], int B[][colb])
{
 
    int C[rowa * rowb][cola * colb];
 
    // i loops till rowa
    for (int i = 0; i < rowa; i++) {
 
        // k loops till rowb
        for (int k = 0; k < cola; k++) {
 
            // j loops till cola
            for (int j = 0; j < rowb; 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 * rowb + k][j * colb + l]
                        = A[i][j] * B[k][l];
                }
            }
        }
    }
 
    for (int i = 0; i < rowa * rowb; i++) {
        for (int j = 0; j < cola * colb; j++) {
            cout << C[i][j] << " ";
        }
        cout << endl;
    }
}
 
// Driver Code
int main()
{
    int A[3][2] = { { 1, 2 }, { 3, 4 }, { 1, 0 } },
        B[2][3] = { { 0, 5, 2 }, { 6, 7, 3 } };
 
    Kroneckerproduct(A, B);
    return 0;
}
 
// This code is contributed by shubhamsingh10

C




// C code to find the Kronecker Product of two
// matrices and stores it as matrix C
#include <stdio.h>
 
// rowa and cola are no of rows and columns
// of matrix A
// rowb and colb are no of rows and columns
// of matrix B
const int cola = 2, rowa = 3, colb = 3, rowb = 2;
 
// Function to computes the Kronecker Product
// of two matrices
void Kroneckerproduct(int A[][cola], int B[][colb])
{
 
    int C[rowa * rowb][cola * colb];
 
    // i loops till rowa
    for (int i = 0; i < rowa; i++) {
 
        // k loops till rowb
        for (int k = 0; k < cola; k++) {
 
            // j loops till cola
            for (int j = 0; j < rowb; 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 * rowb + k][j * colb + l]
                        = A[i][j] * B[k][l];
                }
            }
        }
    }
    for (int i = 0; i < rowa * rowb; i++) {
        for (int j = 0; j < cola * colb; j++) {
            printf("%d ", C[i][j]);
        }
        printf("\n");
    }
}
 
// Driver Code
int main()
{
    int A[3][2] = { { 1, 2 }, { 3, 4 }, { 1, 0 } },
        B[2][3] = { { 0, 5, 2 }, { 6, 7, 3 } };
 
    Kroneckerproduct(A, B);
    return 0;
}

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 < cola; k++) {
 
                // j loops till cola
                for (int j = 0; j < rowb; 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 * rowb + k][j * colb + l]
                            = A[i][j] * B[k][l];
                    }
                }
            }
        }
        for (int i = 0; i < rowa * rowb; i++) {
            for (int j = 0; j < cola * colb; j++) {
                System.out.print(C[i][j] + " ");
            }
            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.

Python3




# Python 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 B
cola = 2
rowa = 3
colb = 3
rowb = 2;
 
# Function to computes the Kronecker Product
# of two matrices
def Kroneckerproduct(A, B):
 
    C = [[0] * (cola * colb)  for _ in range(rowa * rowb) ]
     
    # i loops till rowa
    for i in range(rowa):
 
        # k loops till rowb
        for k in range(cola):
 
            # j loops till cola
            for j in range(rowb):
 
                # l loops till colb
                for l in range(colb):
 
                    # Each element of matrix A is
                    # multiplied by whole Matrix B
                    # resp and stored as Matrix C
                    C[i * rowb + k][j * colb + l]  = A[i][j] * B[k][l];
                 
    for i in range(rowa * rowb):
        print(*C[i])
     
# Driver Code
A = [[ 1, 2 ], [ 3, 4 ], [ 1, 0 ]];
B = [[ 0, 5, 2 ], [ 6, 7, 3 ]];
 
Kroneckerproduct(A, B);
 
# This code is contributed by phasing17

C#




// Include namespace system
using System;
 
public 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
  public static int cola = 2;
  public static int rowa = 3;
  public static int colb = 3;
  public static int rowb = 2;
  // Function to computes the Kronecker Product
  // of two matrices
  public static void Kroneckerproduct(int[,] A, int[,] B)
  {
    int[,] C = new int[GFG.rowa * GFG.rowb,GFG.cola * GFG.colb];
    // i loops till rowa
    for (int i = 0; i < GFG.rowa; i++)
    {
      // k loops till rowb
      for (int k = 0; k < GFG.cola; k++)
      {
        // j loops till cola
        for (int j = 0; j < GFG.rowb; j++)
        {
          // l loops till colb
          for (int l = 0; l < GFG.colb; l++)
          {
            // Each element of matrix A is
            // multiplied by whole Matrix B
            // resp and stored as Matrix C
            C[i * GFG.rowb + k,j * GFG.colb + l] = A[i,j] * B[k,l];
          }
        }
      }
    }
    for (int i = 0; i < GFG.rowa * GFG.rowb; i++)
    {
      for (int j = 0; j < GFG.cola * GFG.colb; j++)
      {
        Console.Write(C[i,j].ToString() + " ");
      }
      Console.WriteLine();
    }
  }
 
  // Driver program
  public static void Main(String[] args)
  {
    int[,] A = {{1, 2}, {3, 4}, {1, 0}};
    int[,] B = {{0, 5, 2}, {6, 7, 3}};
    GFG.Kroneckerproduct(A, B);
  }
}
 
// This code is contributed by aadityaburujwale.

Javascript




// JS 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 B
let cola = 2, rowa = 3, colb = 3, rowb = 2;
 
// Function to computes the Kronecker Product
// of two matrices
function Kroneckerproduct(A, B)
{
 
    let C = new Array(rowa * rowb)
    for (var i = 0; i < rowa * rowb; i++)
        C[i] = new Array(cola * colb)
 
    // i loops till rowa
    for (let i = 0; i < rowa; i++) {
 
        // k loops till rowb
        for (let k = 0; k < cola; k++) {
 
            // j loops till cola
            for (let j = 0; j < rowb; j++) {
 
                // l loops till colb
                for (let l = 0; l < colb; l++) {
 
                    // Each element of matrix A is
                    // multiplied by whole Matrix B
                    // resp and stored as Matrix C
                    C[i * rowb + k][j * colb + l]
                        = A[i][j] * B[k][l];
                }
            }
        }
    }
 
    for (let i = 0; i < rowa * rowb; i++) {
        for (let j = 0; j < cola * colb; j++) {
            process.stdout.write(C[i][j] + " ");
        }
        console.log()
    }
}
 
// Driver Code
let A = [[ 1, 2 ], [ 3, 4 ], [ 1, 0 ]];
let B = [[ 0, 5, 2 ], [ 6, 7, 3 ]];
 
Kroneckerproduct(A, B);
 
// This code is contributed by phasing17

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)
Auxiliary Space: O((rowa * rowb) * (cola * colb))


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