# Kronecker Product of two matrices

• Difficulty Level : Easy
• Last Updated : 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:

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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++ 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 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 = { { 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

 // 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 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 = { { 1, 2 }, { 3, 4 }, { 1, 0 } },        B = { { 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 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

 # 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 = 1A = 2A = 3A = 4A = 1A = 0 B = 0B = 5B = 2B = 6B = 7B = 3 Kroneckerproduct( A , B ) # This code is contributed by Saloni.

## C#

 // 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

 

## Javascript

 

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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