Kronecker Product of two matrices - GeeksforGeeks

03 May, 2021
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 :  
C++
C
Java
Python3
C#
PHP
Javascript
// C++ code to find the Kronecker Product of two// matrices and stores it as matrix C#include <iostream>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 Bconst int cola = 2, rowa = 3, colb = 3, rowb = 2; // Function to computes the Kronecker Product// of two matricesvoid 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 Codeint 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 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 Bconst int cola = 2, rowa = 3, colb = 3, rowb = 2; // Function to computes the Kronecker Product// of two matricesvoid 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 Codeint 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 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.
# 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 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[0][0] = 1A[0][1] = 2A[1][0] = 3A[1][1] = 4A[2][0] = 1A[2][1] = 0 B[0][0] = 0B[0][1] = 5B[0][2] = 2B[1][0] = 6B[1][1] = 7B[1][2] = 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 Cusing 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.
<?php// PHP code to find the// Kronecker Product of two // 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 matricesfunction Kroneckerproduct($A, $B){    global $cola;    global $rowa;    global $colb;    global $rowb;      //$C[$rowa * $rowb][$cola * $colb];    $C;     // i loops till rowa    for ( $i = 0; $i < $rowa; $i++)    {         // k loops till rowb        for ($k = 0; $k < $rowb; $k++)        {             // j loops till cola            for ( $j = 0; $j < $cola; $j++)             {                 // l loops till colb                for ($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][$l];                    echo ($C[$i + $l + 1][$j + $k + 1]), "\t" ;                }            }        echo "\n";        }    }} // Driver Code$A = array (array (1, 2),            array (3, 4),            array (1, 0));$B = array (array (0, 5, 2),            array (6, 7, 3)); Kroneckerproduct($A, $B); // This code is contributed by ajit?>
<script>    // Javascript 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(let i = 0; i < (rowa * rowb); i++)        {            C[i] = new Array(cola * colb);            for(let j = 0; j < (cola * colb); j++)            {                C[i][j] = 0;            }        }               // i loops till rowa        for (let i = 0; i < rowa; i++)        {                   // k loops till rowb            for (let k = 0; k < rowb; k++)            {                       // j loops till cola                for (let j = 0; j < cola; 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 + l + 1][j + k + 1] = A[i][j] * B[k][l];                        document.write( C[i + l + 1][j + k + 1]+" ");                    }                }                document.write("</br>");            }        }    }         let A = [ [ 1, 2 ],             [ 3, 4 ],             [ 1, 0 ] ];                             let B = [ [ 0, 5, 2 ],                  [ 6, 7, 3 ] ];     Kroneckerproduct(A, B);     </script>
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
 
nitin mittal
jit_t
nidhi_biet
SHUBHAMSINGH10
rameshtravel07
Arrays
Matrix
Arrays
Matrix
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