# Kronecker Product of two matrices

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


## Recommended: Please solve it on PRACTICE first, before moving on to the solution.

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

 // C++ code to find the Kronecker Product of two  // matrices and stores it as matrix C  #include  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 < 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];                      cout << C[i + l + 1][j + k + 1] << " ";                  }              }              cout << endl;          }      }  }     // Driver Code  int main()  {      int A = { { 1, 2 }, { 3, 4 }, { 1, 0 } },          B = { { 0, 5, 2 }, { 6, 7, 3 } };         Kroneckerproduct(A, B);      return 0;  }     //This code is contributed by shubhamsingh10

 // C code to find the Kronecker Product of two  // matrices and stores it as matrix C  #include     // 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 < 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];                      printf("%d\t", C[i + l + 1][j + k + 1]);                  }              }              printf("\n");          }      }  }     // Driver Code  int main()  {      int A = { { 1, 2 }, { 3, 4 }, { 1, 0 } },          B = { { 0, 5, 2 }, { 6, 7, 3 } };         Kroneckerproduct(A, B);      return 0;  }

 // 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.

 # 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 B  cola = 2 rowa = 3 colb = 3 rowb = 2     # Function to computes the Kronecker Product  # of two matrices     def 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 ("\n")                # 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 = 1 A = 2 A = 3 A = 4 A = 1 A = 0    B = 0 B = 5 B = 2 B = 6 B = 7 B = 3    Kroneckerproduct( A , B )     # This code is contributed by Saloni.

 // C# code to find the Kronecker Product of  // two matrices and stores it as matrix C  using System;     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;      static int 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];                          Console.Write( C[i + l + 1,                                          j + k + 1] + " ");                      }                  }                  Console.WriteLine();              }          }      }             // Driver Code      public static void Main ()      {          int [,]A = {{1, 2},                     {3, 4},                      {1, 0}};                                     int [,]B = {{0, 5, 2},                     {6, 7, 3}};                 Kroneckerproduct(A, B);       }  }     // This code is contributed by nitin mittal.

 

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


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