Given two matrices, the task to multiply them. Matrices can either be square or rectangular.
Examples:
Input : mat1[][] = {{1, 2},
{3, 4}}
mat2[][] = {{1, 1},
{1, 1}}
Output : {{3, 3},
{7, 7}}
Input : mat1[][] = {{2, 4},
{3, 4}}
mat2[][] = {{1, 2},
{1, 3}}
Output : {{6, 16},
{7, 18}}
Multiplication of Square Matrices :
The below program multiplies two square matrices of size 4*4, we can change N for different dimensions.
Javascript
<script> // Javascript program to multiply // two square matrices. const N = 4; // This function multiplies // mat1[][] and mat2[][], and // stores the result in res[][] function multiply(mat1, mat2, res) { let i, j, k; for (i = 0; i < N; i++) { for (j = 0; j < N; j++) { res[i][j] = 0; for (k = 0; k < N; k++) res[i][j] += mat1[i][k] * mat2[k][j]; } } } // Driver Code let i, j; // To store result let res = new Array(N); for (let k = 0; k < N; k++) res[k] = new Array(N); let mat1 = [ [ 1, 1, 1, 1 ], [ 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 4, 4, 4 ] ]; let mat2 = [ [ 1, 1, 1, 1 ], [ 2, 2, 2, 2 ], [ 3, 3, 3, 3 ], [ 4, 4, 4, 4 ] ]; multiply(mat1, mat2, res); document.write("Result matrix is <br>"); for (i = 0; i < N; i++) { for (j = 0; j < N; j++) document.write(res[i][j] + " "); document.write("<br>"); } </script> |
Output
Result matrix is 10 10 10 10 20 20 20 20 30 30 30 30 40 40 40 40
Time complexity: O(n3). It can be optimized using Strassen’s Matrix Multiplication
Auxiliary Space: O(n2)
Multiplication of Rectangular Matrices :
We use pointers in C to multiply to matrices. Please refer to the following post as a prerequisite of the code.
How to pass a 2D array as a parameter in C?
Javascript
<script> // Javascript 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 = new Array(m1); for (i = 0; i < m1; i++) res[i] = new Array(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++) { document.write(res[i][j] + " "); } document.write("<br>"); } } // Driver code let mat1 = [ [ 2, 4 ], [ 3, 4 ] ]; let mat2 = [ [ 1, 2 ], [ 1, 3 ] ]; let m1 = 2, m2 = 2, n1 = 2, n2 = 2; // Function call multiply(m1, m2, mat1, n1, n2, mat2); </script> |
Output
6 16 7 18
Time complexity: O(n3). It can be optimized using Strassen’s Matrix Multiplication
Auxiliary Space: O(m1 * n2)
Please refer complete article on Program to multiply two matrices for more details!
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