In Java, Matrix Multiplication is a complex operation, unlike multiplying two constant numbers. In this article, we will learn How to perform matrix multiplication in Java.
Example of Multiplication of Two Matrices
Input:
A[][] = {{1, 2}, {3, 4}}
B[][] = {{1, 1}, {1, 1}}Output:
{{3, 3},
{7, 7}}Input:
A[][] = {{2, 4}, {3, 4}}
B[][] = {{1, 2}, {1, 3}}Output:
{{6, 16},
{7, 18}}
Approach:
- Take the two matrices to be multiplied
- Check if the two matrices are compatible to be multiplied
- Create a new Matrix to store the product of the two matrices
- Traverse each element of the two matrices and multiply them. Store this product in the new matrix at the corresponding index.
- Print the final product matrix
Note: Two matrices are multiplicable if the number of coloumns in the first matrix is equal to the number of rows in the second matrix
Program for Matrix Multiplication in Java
Below is the implementation of the above approach:
Java
// Java program to multiply// two matrices of any size.import java.io.*;// Driver Classclass GFG { // Function to print Matrix static void printMatrix(int M[][], int rowSize, int colSize) { for (int i = 0; i < rowSize; i++) { for (int j = 0; j < colSize; j++) System.out.print(M[i][j] + " "); System.out.println(); } } // Function to multiply // two matrices A[][] and B[][] static void multiplyMatrix(int row1, int col1, int A[][], int row2, int col2, int B[][]) { int i, j, k; // Print the matrices A and B System.out.println("\nMatrix A:"); printMatrix(A, row1, col1); System.out.println("\nMatrix B:"); printMatrix(B, row2, col2); // Check if multiplication is Possible if (row2 != col1) { System.out.println( "\nMultiplication Not Possible"); return; } // Matrix to store the result // The product matrix will // be of size row1 x col2 int C[][] = new int[row1][col2]; // Multiply the two matrices for (i = 0; i < row1; i++) { for (j = 0; j < col2; j++) { for (k = 0; k < row2; k++) C[i][j] += A[i][k] * B[k][j]; } } // Print the result System.out.println("\nResultant Matrix:"); printMatrix(C, row1, col2); } // Driver code public static void main(String[] args) { int row1 = 4, col1 = 3, row2 = 3, col2 = 4; int A[][] = { { 1, 1, 1 }, { 2, 2, 2 }, { 3, 3, 3 }, { 4, 4, 4 } }; int B[][] = { { 1, 1, 1, 1 }, { 2, 2, 2, 2 }, { 3, 3, 3, 3 } }; multiplyMatrix(row1, col1, A, row2, col2, B); }} |
Matrix A: 1 1 1 2 2 2 3 3 3 4 4 4 Matrix B: 1 1 1 1 2 2 2 2 3 3 3 3 Resultant Matrix: 6 6 6 6 12 12 12 12 18 18 18 18 24 24 24 24
The complexity of the above method
Time Complexity: O(M*N*P) for the traversal of the nested loops. In case, of the specific example with multiplication of 4×3 matrix and 3×4 matrix, M=P, thats why the time complexity becomes = O(M2*N).
Auxiliary Space: O(M*N), as we are using extra space.
