Given two matrices, the task is to multiply them. Matrices can either be square or rectangular:
Examples:
(Square Matrix Multiplication)
Input: mat1[m][n] = { {1, 1}, {2, 2} }
mat2[n][p] = { {1, 1}, {2, 2} }
Output: result[m][p] = { {3, 3}, {6, 6} }(Rectangular Matrix Multiplication)
Input: mat1[3][2] = { {1, 1}, {2, 2}, {3, 3} }
mat2[2][3] = { {1, 1, 1}, {2, 2, 2} }
Output: result[3][3] = { {3, 3, 3}, {6, 6, 6}, {9, 9, 9} }
Multiplication of two Square or Rectangular Matrices:
- The number of columns in Matrix-1 must be equal to the number of rows in Matrix-2.
- Output of multiplication of Matrix-1 and Matrix-2, results with equal to the number of rows of Matrix-1 and the number of columns of Matrix-2 i.e. rslt[R1][C2]
Below is the implementation of the multiplication of two matrices:
C
// C program to multiply two matrices #include <stdio.h> #include <stdlib.h> // Edit MACROs here, according to your Matrix Dimensions for // mat1[R1][C1] and mat2[R2][C2] #define R1 2 // number of rows in Matrix-1 #define C1 2 // number of columns in Matrix-1 #define R2 2 // number of rows in Matrix-2 #define C2 2 // number of columns in Matrix-2 void mulMat(int mat1[][C1], int mat2[][C2]) { int rslt[R1][C2]; printf("Multiplication of given two matrices is:\n"); for (int i = 0; i < R1; i++) { for (int j = 0; j < C2; j++) { rslt[i][j] = 0; for (int k = 0; k < R2; k++) { rslt[i][j] += mat1[i][k] * mat2[k][j]; } printf("%d\t", rslt[i][j]); } printf("\n"); } } // Driver code int main() { // R1 = 4, C1 = 4 and R2 = 4, C2 = 4 (Update these // values in MACROs) int mat1[R1][C1] = { { 1, 1 }, { 2, 2 } }; int mat2[R2][C2] = { { 1, 1 }, { 2, 2 } }; if (C1 != R2) { printf("The number of columns in Matrix-1 must be " "equal to the number of rows in " "Matrix-2\n"); printf("Please update MACROs value according to " "your array dimension in " "#define section\n"); exit(EXIT_FAILURE); } // Function call mulMat(mat1, mat2); return 0; } // This code is contributed by Manish Kumar (mkumar2789) |
C++
// C++ program to multiply two matrices #include <bits/stdc++.h> using namespace std; // Edit MACROs here, according to your Matrix Dimensions for // mat1[R1][C1] and mat2[R2][C2] #define R1 2 // number of rows in Matrix-1 #define C1 2 // number of columns in Matrix-1 #define R2 2 // number of rows in Matrix-2 #define C2 2 // number of columns in Matrix-2 void mulMat(int mat1[][C1], int mat2[][C2]) { int rslt[R1][C2]; cout << "Multiplication of given two matrices is:\n"; for (int i = 0; i < R1; i++) { for (int j = 0; j < C2; j++) { rslt[i][j] = 0; for (int k = 0; k < R2; k++) { rslt[i][j] += mat1[i][k] * mat2[k][j]; } cout << rslt[i][j] << "\t"; } cout << endl; } } // Driver code int main() { // R1 = 4, C1 = 4 and R2 = 4, C2 = 4 (Update these // values in MACROs) int mat1[R1][C1] = { { 1, 1 }, { 2, 2 } }; int mat2[R2][C2] = { { 1, 1 }, { 2, 2 } }; if (C1 != R2) { cout << "The number of columns in Matrix-1 must " "be equal to the number of rows in " "Matrix-2" << endl; cout << "Please update MACROs according to your " "array dimension in #define section" << endl; exit(EXIT_FAILURE); } // Function call mulMat(mat1, mat2); return 0; } // This code is contributed by Manish Kumar (mkumar2789) |
Java
// C++ program to multiply two matrices import java.io.*; import java.util.*; class GFG { static int R1 = 2; // number of rows in Matrix-1 static int C1 = 2; // number of columns in Matrix-1 static int R2 = 2; // number of rows in Matrix-2 static int C2 = 2; // number of columns in Matrix-2 // This function multiplies mat1[][] // and mat2[][], and stores the result // in res[][] static void mulMat(int[][] mat1, int[][] mat2) { // To store result int[][] rslt = new int[R1][C2]; System.out.println( "Multiplication of given two matrices is:"); int i, j, k; for (i = 0; i < R1; i++) { for (j = 0; j < C2; j++) { rslt[i][j] = 0; for (k = 0; k < R2; k++) rslt[i][j] += mat1[i][k] * mat2[k][j]; System.out.print(rslt[i][j] + " "); } System.out.println(""); } } // Driver code public static void main(String[] args) { int[][] mat1 = { { 1, 1 }, { 2, 2 } }; int[][] mat2 = { { 1, 1 }, { 2, 2 } }; if (C1 != R2) { System.out.println( "The number of columns in Matrix-1 must be equal to the number of rows in Matrix-2"); System.out.println( "Please update the global variables according to your array dimension"); } else { // Function call mulMat(mat1, mat2); } } } // This code is contributed by shruti456rawal |
Python3
# Python3 program to multiply two matrices def mulMat(mat1, mat2, R1, R2, C1, C2): # List to store matrix multiplication result rslt = [[0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0], [0, 0, 0, 0]] for i in range(0, R1): for j in range(0, C2): for k in range(0, R2): rslt[i][j] += mat1[i][k] * mat2[k][j] print("Multiplication of given two matrices is:") for i in range(0, R1): for j in range(0, C2): print(rslt[i][j], end=" ") print("\n", end="") # Driver code if __name__ == '__main__': R1 = 2 R2 = 2 C1 = 2 C2 = 2 # First matrix. M is a list mat1 = [[1, 1], [2, 2]] # Second matrix. N is a list mat2 = [[1, 1], [2, 2]] if C1 != R2: print("The number of columns in Matrix-1 must be equal to the number of rows in " + "Matrix-2", end='') print("\n", end='') print("Please update MACROs according to your array dimension in #define section", end='') print("\n", end='') else: # Call matrix_multiplication function mulMat(mat1, mat2, R1, R2, C1, C2) # This code is contributed by Aarti_Rathi |
C#
// C# program to multiply two matrices using System; class GFG { static int R1 = 2; // number of rows in Matrix-1 static int C1 = 2; // number of columns in Matrix-1 static int R2 = 2; // number of rows in Matrix-2 static int C2 = 2; // number of columns in Matrix-2 // This function multiplies mat1[][] // and mat2[][], and stores the result // in res[][] static void mulMat(int[, ] mat1, int[, ] mat2) { // To store result int[, ] rslt = new int[R1, C2]; Console.WriteLine( "Multiplication of given two matrices is:"); int i, j, k; for (i = 0; i < R1; i++) { for (j = 0; j < C2; j++) { rslt[i, j] = 0; for (k = 0; k < R2; k++) rslt[i, j] += mat1[i, k] * mat2[k, j]; Console.Write(rslt[i, j] + "\t"); } Console.WriteLine(); } } // Driver code public static void Main() { int[, ] mat1 = { { 1, 1 }, { 2, 2 } }; int[, ] mat2 = { { 1, 1 }, { 2, 2 } }; if (C1 != R2) { Console.WriteLine( "The number of columns in Matrix-1 must be equal to the number of rows in Matrix-2"); Console.WriteLine( "Please update MACROs according to your array dimension in #define section"); } else { mulMat(mat1, mat2); } } } // This code is contributed by Aarti_Rathi |
Javascript
var R1 = 2; // number of rows in Matrix-1 var C1 = 2; // number of columns in Matrix-1 var R2 = 2; // number of rows in Matrix-2 var C2 = 2; // number of columns in Matrix-2 // This function multiplies mat1[][] // and mat2[][], and stores the result // in res[][] function mulMat(mat1, mat2) { // To store result var rslt = Array(R1).fill(0).map(()=>new Array(C2).fill(0)); console.log("Multiplication of given two matrices is:"); var i = 0; var j = 0; var k = 0; for (i = 0; i < R1; i++) { for (j = 0; j < C2; j++) { rslt[i][j] = 0; for (k = 0; k < R2; k++) { rslt[i][j] += mat1[i][k] * mat2[k][j]; } console.log(rslt[i][j] + " "); } console.log(""); } } // Driver program var mat1 = [[1, 1], [2, 2]]; var mat2 = [[1, 1], [2, 2]]; if (C1 != R2) { console.log("The number of columns in Matrix-1 must be equal to the number of rows in Matrix-2"); console.log("Please update the global variables according to your array dimension"); } else { mulMat(mat1, mat2); } // This code is contributed by Aarti_Rathi |
Output
Multiplication of given two matrices is: 3 3 6 6
Time complexity: O(R1 * C2 * R2) for given matrices mat1[R1][C1] and mat2[R2][C2]
Auxiliary space: O(R1 * C2)
Multiplication of Rectangular Matrices using Pointers in C/C++:
To solve the problem follow the below idea:
We use pointers in C/C++ to multiply matrices
Prerequisite: How to pass a 2D array as a parameter in C?
Below is the implementation of the above approach:
C++
// C++ program to multiply two // rectangular matrices #include <bits/stdc++.h> using namespace std; // Multiplies two matrices mat1[][] // and mat2[][] and prints result. // (m1) x (m2) and (n1) x (n2) are // dimensions of given matrices. void multiply(int m1, int m2, int mat1[][2], int n1, int n2, int mat2[][2]) { int x, i, j; int res[m1][n2]; for (i = 0; i < m1; i++) { for (j = 0; j < n2; j++) { res[i][j] = 0; for (x = 0; x < m2; x++) { *(*(res + i) + j) += *(*(mat1 + i) + x) * *(*(mat2 + x) + j); } } } for (i = 0; i < m1; i++) { for (j = 0; j < n2; j++) { cout << *(*(res + i) + j) << " "; } cout << "\n"; } } // Driver code int main() { int mat1[][2] = { { 1, 1 }, { 2, 2 } }; int mat2[][2] = { { 1, 1 }, { 2, 2 } }; int m1 = 2, m2 = 2, n1 = 2, n2 = 2; // Function call multiply(m1, m2, mat1, n1, n2, mat2); return 0; } // This code is contributed // by Akanksha Rai(Abby_akku) |
C
// C program to multiply two rectangular matrices #include <stdio.h> // Multiplies two matrices mat1[][] and mat2[][] // and prints result. // (m1) x (m2) and (n1) x (n2) are dimensions // of given matrices. void multiply(int m1, int m2, int mat1[][m2], int n1, int n2, int mat2[][n2]) { int x, i, j; int res[m1][n2]; for (i = 0; i < m1; i++) { for (j = 0; j < n2; j++) { res[i][j] = 0; for (x = 0; x < m2; x++) { *(*(res + i) + j) += *(*(mat1 + i) + x) * *(*(mat2 + x) + j); } } } for (i = 0; i < m1; i++) { for (j = 0; j < n2; j++) { printf("%d ", *(*(res + i) + j)); } printf("\n"); } } // Driver code int main() { int mat1[][2] = { { 1, 1 }, { 2, 2 } }; int mat2[][2] = { { 1, 1 }, { 2, 2 } }; int m1 = 2, m2 = 2, n1 = 2, n2 = 2; // Function call multiply(m1, m2, mat1, n1, n2, mat2); return 0; } |
Java
// JAVA program to multiply two // rectangular matrices import java.io.*; import java.lang.*; import java.util.*; // Multiplies two matrices mat1[][] // and mat2[][] and prints result. // (m1) x (m2) and (n1) x (n2) are // dimensions of given matrices. public class GFG { public static void multiply(int m1, int m2, int mat1[][], int n1, int n2, int mat2[][]) { int x, i, j; int res[][] = new int[m1][n2]; for (i = 0; i < m1; i++) { for (j = 0; j < n2; j++) { res[i][j] = 0; for (x = 0; x < m2; x++) { res[i][j] += mat1[i][x] * mat2[x][j]; } } } for (i = 0; i < m1; i++) { for (j = 0; j < n2; j++) { System.out.print(res[i][j] + " "); } System.out.println(); } } // Driver code public static void main(String[] args) { int m1 = 2, m2 = 2, n1 = 2, n2 = 2; int mat1[][] = new int[][] { { 1, 1 }, { 2, 2 } }; int mat2[][] = new int[][] { { 1, 1 }, { 2, 2 } }; // Function call multiply(m1, m2, mat1, n1, n2, mat2); } } // This code is contributed by ishankhandelwals. |
Python3
# Python program to multiply two # rectangular matrices # Multiplies two matrices mat1[][] # and mat2[][] and prints result. # (m1) x (m2) and (n1) x (n2) are # dimensions of given matrices. def multiply(m1, m2, mat1, n1, n2, mat2): res = [[0 for x in range(n2)] for y in range(m1)] for i in range(m1): for j in range(n2): res[i][j] = 0 for x in range(m2): res[i][j] += mat1[i][x] * mat2[x][j] for i in range(m1): for j in range(n2): print(res[i][j], end=" ") print() # Driver code m1 = 2m2 = 2n1 = 2n2 = 2mat1 = [[1, 1], [2, 2]] mat2 = [[1, 1], [2, 2]] # Function call multiply(m1, m2, mat1, n1, n2, mat2) # This code is contributed by Tapesh(tapeshdua420) |
C#
// C# program to multiply two // rectangular matrices using System; class Program { // Driver code static void Main(string[] args) { int m1 = 2, m2 = 2, n1 = 2, n2 = 2; int[, ] mat1 = new int[, ] { { 1, 1 }, { 2, 2 } }; int[, ] mat2 = new int[, ] { { 1, 1 }, { 2, 2 } }; // Function call multiply(m1, m2, mat1, n1, n2, mat2); } // Multiplies two matrices mat1[][] // and mat2[][] and prints result. // (m1) x (m2) and (n1) x (n2) are // dimensions of given matrices. static void multiply(int m1, int m2, int[, ] mat1, int n1, int n2, int[, ] mat2) { int x, i, j; int[, ] res = new int[m1, n2]; for (i = 0; i < m1; i++) { for (j = 0; j < n2; j++) { res[i, j] = 0; for (x = 0; x < m2; x++) { res[i, j] += mat1[i, x] * mat2[x, j]; } } } for (i = 0; i < m1; i++) { for (j = 0; j < n2; j++) { Console.Write(res[i, j] + " "); } Console.WriteLine(); } } } // This code is contributed by Tapesh(tapeshdua420) |
Javascript
// JS program to multiply two // rectangular matrices // Multiplies two matrices mat1[][] // and mat2[][] and prints result. // (m1) x (m2) and (n1) x (n2) are // dimensions of given matrices. function multiply(m1, m2, mat1, n1, n2, mat2) { let x, i, j; let res = [[0, 0], [0, 0]]; for (i = 0; i < m1; i++) { for (j = 0; j < n2; j++) { // res[i][j] = 0; for (x = 0; x < m2; x++) { res[i][j] += (mat1[i][x] * mat2[x][j]) } } } for (i = 0; i < m1; i++) { for (j = 0; j < n2; j++) { console.log(res[i][j]); } } } // Driver code let mat1 = [[1, 1], [2, 2]]; let mat2 = [[1, 1], [2, 2]]; let m1 = 2, m2 = 2, n1 = 2, n2 = 2; // Function call multiply(m1, m2, mat1, n1, n2, mat2); // This code is contributed by ishankhandelwals. |
Output
3 3 6 6
Time complexity: O(N3)
Auxiliary Space: O(M1 * N2)
Related Article: Strassen’s Matrix Multiplication
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