A square matrix is said to be symmetric matrix if the transpose of the matrix is same as the given matrix. Symmetric matrix can be obtain by changing row to column and column to row.
Examples:
Input : 1 2 3
2 1 4
3 4 3
Output : Yes
Input : 3 5 8
3 4 7
8 5 3
Output : No
A Simple solution is to do following.
1) Create transpose of given matrix.
2) Check if transpose and given matrices are same or not.
Java
// Simple java code for check a matrix is // symmetric or not. import java.io.*; class GFG { static int MAX = 100; // Fills transpose of mat[N][N] in tr[N][N] static void transpose(int mat[][], int tr[][], int N) { for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) tr[i][j] = mat[j][i]; } // Returns true if mat[N][N] is symmetric, else false static boolean isSymmetric(int mat[][], int N) { int tr[][] = new int[N][MAX]; transpose(mat, tr, N); for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (mat[i][j] != tr[i][j]) return false; return true; } // Driver code public static void main (String[] args) { int mat[][] = { { 1, 3, 5 }, { 3, 2, 4 }, { 5, 4, 1 } }; if (isSymmetric(mat, 3)) System.out.println( "Yes"); else System.out.println ( "No"); } } |
Output :
Yes
Time Complexity : O(N x N)
Auxiliary Space : O(N x N)
An Efficient solution to check a matrix is symmetric or not is to compare matrix elements without creating a transpose. We basically need to compare mat[i][j] with mat[j][i].
Java
// Efficient Java code for check a matrix is // symmetric or no import java.io.*; class GFG { static int MAX = 100; // Returns true if mat[N][N] // is symmetric, else false static boolean isSymmetric(int mat[][], int N) { for (int i = 0; i < N; i++) for (int j = 0; j < N; j++) if (mat[i][j] != mat[j][i]) return false; return true; } // Driver code public static void main (String[] args) { int mat[][] = { { 1, 3, 5 }, { 3, 2, 4 }, { 5, 4, 1 } }; if (isSymmetric(mat, 3)) System.out.println( "Yes"); else System.out.println("NO"); } } // |
Output:
Yes
Time Complexity : O(N x N)
Auxiliary Space : O(1)
Please refer complete article on Program to check if a matrix is symmetric for more details!
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