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

 // 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

 // 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

 # 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#

 // 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.

PHP



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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Improved By : nitin mittal, jit_t, nidhi_biet

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