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Java Program to multiply two Matrix .

Java Code Example — Array Programs

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Java Program to multiply two Matrix .

Objective

Write a Java program to multiply two matrices of compatible dimensions.

Algorithm / Approach

  1. Define dimensions for matrix 1 (3x2) and matrix 2 (2x4). The result matrix will be (3x4).
  2. Read input elements for both matrices using nested loops.
  3. Use three nested loops for multiplication. The outer two loops (i, j) traverse the resulting matrix m3.
  4. The innermost loop (k) performs the dot product of the i-th row of m1 and the j-th column of m2.
  5. Accumulate the sum: sum = sum + m1[i][k] * m2[k][j].
  6. Assign sum to m3[i][j] and reset sum = 0.
Matrix.java 
import java.util.Scanner;
class Matrix {
 void mul() {
  Scanner s=new Scanner(System.in);
  int r1 = 3, c1 = 2 ;
  int r2 = 2, c2 = 4, sum =0;
  int m1[][] = new int[r1][c1];
  int m2[][] = new int[r2][c2];
  int m3[][] = new int[r1][c2];
  System.out.println("Enter Elements of Mat1: ");
  for(int i = 0; i< r1; i++) {
   for(int j = 0; j< c1; j++) { 
    m1[i][j] = s.nextInt();
   }
  }
  System.out.println("Enter Elements of Mat2: ");
  for(int i = 0; i< r2; i++) {
   for(int j = 0; j< c2; j++) { 
    m2[i][j] = s.nextInt();
   }
  }
  for(int i = 0; i< r1; i++) {
   for(int j = 0; j< c2; j++) { 
    for(int k = 0; k< r2;k++) {
     sum = sum+m1[i][k]*m2[k][j];
    }
    m3[i][j]= sum;
    sum = 0;
   }
  }
  System.out.println("Product of the matrix: ");
  for(int i = 0; i< r1; i++) {
   for(int j = 0; j< c2; j++) { 
    System.out.print(m3[i][j]+"  ");
   }
   System.out.println();
  }
 }
 public static void main(String[] a)
 {
  Matrix m = new Matrix();
  m.mul();
 }
}

Expected Output

Enter Elements of Mat1:
1 4
2 3
4 5
Enter Elements of Mat2:
1 2 3 4
1 3 4 5
Product of the matrix:
5  14  19  24
5  13  18  23
9  23  32  41

Explanation of the Program

  • Matrix multiplication is much more complex than addition. You don't just multiply corresponding elements.
  • Instead, you must calculate the dot product. To find the value for row 1, column 1 of the result, you multiply each element of row 1 in the first matrix by each corresponding element of column 1 in the second matrix, and add them all together.
  • This requires three layers of nested loops, making it an expensive operation computationally.

Complexity

Time Complexity O(r1 * c2 * c1) - Roughly O(N3) for square matrices.
Space Complexity O(r1 * c2) - Memory required for the resulting matrix.

Common Mistakes

  • Trying to multiply matrices with incompatible dimensions. The number of columns in the first matrix MUST equal the number of rows in the second matrix.
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