A symmetric matrix is a square matrix in which the transpose of the square matrix is the same as the original square matrix. A square matrix is a matrix in which the number of columns is the same as the number of rows. If the matrix is a symmetric matrix then it is also a square matrix but vice versa isn’t true. Matrix is simply considered as 2D arrays for action to be performed. Here, we are going to see the approach to check if the entered square matrix is symmetric or not.
Illustration:
Input : 6 5 2
5 0 9
2 9 3
Output: The matrix is symmetric
Input : 6 1 2
5 0 9
2 9 3
Output: The matrix is not symmetric
Approach:
- Take the matrix as an input from the user
- Find transpose of the matrix
- Compare two matrices
- If the two matrices is the same then it is symmetric otherwise it’s not.
Implementation:
Example
Java
// Java Program to check whether matrix is// symmetric or not// Importing all classes of// java.util packageimport java.util.*;// Classpublic class GFG { // Matrix 1 // Method to check whether the matrix is // symmetric or asymmetric static void checkSymmetric(int mat[][], int row, int col) { int i, j, flag = 1; // Display message System.out.println("The matrix formed is:"); // Nested for loop for matrix iteration // Outer loop for rows for (i = 0; i < row; i++) { // Inner loop for columns for (j = 0; j < col; j++) { // Print matrix System.out.print(mat[i][j] + "\t"); } System.out.println(""); } // Matrix 2 // Finding transpose of the matrix int[][] transpose = new int[row][col]; // Again, nested for loop for matrix iteration // Outer loop for rows for (i = 0; i < row; i++) { // Inner loop for columns for (j = 0; j < col; j++) { // Print matrix elements transpose[j][i] = mat[i][j]; } } // Condition check over Matrix 1 with Matrix 2 if (row == col) { // Outer loop for rows for (i = 0; i < row; i++) { // Inner loop for columns for (j = 0; j < col; j++) { // Comparing two matrices if (mat[i][j] != transpose[i][j]) { flag = 0; break; } } // Setting a flag value for symmetric matrix if (flag == 0) { // Display message System.out.print( "\nThe matrix is not symmetric"); break; } } // Setting a flag value different from above // for symmetric matrix if (flag == 1) { // Display message System.out.print( "\nThe matrix is symmetric"); } } // If it isn't a square matrix // then it can't be a symmetric matrix else { // Display message System.out.print( "\nThe matrix is not symmetric"); } } // Main driver method public static void main(String args[]) { // Taking input from the user Scanner sc = new Scanner(System.in); // Declaring variables and setting flag to 1 int i, j, row, col, flag = 1; // Taking input from the user System.out.print("Enter the number of rows:"); row = sc.nextInt(); // Display message System.out.print("Enter the number of columns:"); // Reading matrix elements individually using // nextInt() method col = sc.nextInt(); // Declaring a 2D array(matrix) int[][] mat = new int[row][col]; // Display message System.out.println("Enter the matrix elements:"); // Nested for loop for traversing matrix // Outer loop for rows for (i = 0; i < row; i++) { // Inner loop for columns for (j = 0; j < col; j++) { // Print matrix element mat[i][j] = sc.nextInt(); } } // calling function made above to check // whether matrix is symmetric or not checkSymmetric(mat, row, col); }} |
Output: Below both symmetricity and asymmetricity is checked as follows:
