Java program to multiply two matrices has been shown here. Matrix $[A]_{m \times n}$ can be multiplied with matrix $[B]_{p \times q}$, iff $n = p$ i.e. the number of columns of the first matrix should to be equal to the number of rows in the second matrix. The order of the resultant matrix $C$ would be $m \times q$.
Algorithm, pseudocode and time complexity of the program have also been shown below.
1. Algorithm for matrix multiplication
1. Take two matrice $A_{m\times n}$ and $B_{p\times q}$ as input.
2. Declare another matrix $C_{m\times q}$ and initailize it with 0.
3. Check if $n = p$
4. If step [3] is false then display "Matrices can not be multiplied!" and go to step [8]
5. If step [3] is true, then
6. Repeat for each $i \in [0, m - 1]$
6.1. Repeat for each $j \in [0, q - 1]$
6.1.1. Repeat for each $k \in [0, p - 1]$
6.1.1.1. Perform $C[i][j] = C[i][j] + A[i][k] * B[k][j]$
7. Display $C_{m\times q}$ as the resultant matrix.
8. Exit program.
2. Pseudocode for matrix multiplication
Input: Two matrices $A_{m\times n}$ and $B_{p\times q}$
Output: $A * B$
1. Procedure matrixMultiplication($A_{m\times n}$, $B_{p\times q}$):
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11. End Procedure
3. Time Complexity for matrix multiplication
Time Complexity: O($n^3$)
Where $n$ is the row and column size of two matrices.
4. Java Program for matrix multiplication
/**************************************** alphabetacoder.com Java Program for Matrix Multiplication *****************************************/ import java.util.Scanner; class Main { public static void main(String args[]) { // declare object of Scanner class Scanner sc = new Scanner(System.in); // declare variables int m, n, p, q, i, j, k; int A[][] = new int[10][10]; int B[][] = new int[10][10]; int C[][] = new int[10][10]; //take input of the order of first matrix System.out.print("Enter the number of row and column of first matrix: "); m = sc.nextInt(); n = sc.nextInt(); //take input of the first matrix System.out.println("Enter the first matrix of order " + m + " x " + n + " = "); for (i = 0; i < m; i++) for (j = 0; j < n; j++) A[i][j] = sc.nextInt(); //take input of the order of second matrix System.out.print("Enter the number of row and column of second matrix: "); p = sc.nextInt(); q = sc.nextInt(); //take input of the second matrix System.out.println("Enter the second matrix of order " + p + " x " + q + " = "); for (i = 0; i < p; i++) for (j = 0; j < q; j++) B[i][j] = sc.nextInt(); // check if number of columns in first matrix // is same as number of rows in second matrix. // If not, then matrices can not be multiplied if (n != p) System.out.print("\nMatrices can not be multiplied!"); else { // do matrix multiplication for (i = 0; i < m; i++) { for (j = 0; j < q; j++) { for (k = 0; k < p; k++) C[i][j] += A[i][k] * B[k][j]; } } System.out.println("The resultant matrix after multiplication:"); //display the result for (i = 0; i < m; i++) { for (j = 0; j < q; j++) { System.out.print(C[i][j] + " "); } //new line System.out.println(""); } } } }
Output
Enter the number of row and column of first matrix: 2 2
Enter the first matrix of order 2 x 2 =
8 10
6 9
Enter the number of row and column of second matrix: 2 3
Enter the second matrix of order 2 x 3 =
2 7 8
0 4 1
The resultant matrix after multiplication:
16 96 74
12 78 57