C Program To Check whether Matrix is Skew Symmetric or not

A Skew Symmetric Matrix or Anti-Symmetric Matrix is a square matrix whose transpose is negative to that of the original matrix. If the entry in the i^th row and j^th column of a matrix is a[i][j], i.e. if A = (a[i][j]) then the skew symmetric condition is -A = -a[j][i].

Examples :

Input : matrix:     0   5  -4          
                   -5   0   1                            
                    4  -1   0                            

Output:  
Transpose matrix:   0  -5   4
                    5   0   1
                   -4   1   0
Skew Symmetric matrix

Steps:

Find the transpose of the input matrix.
If the input matrix is equal to the negative of its transpose matrix, then the matrix is Skew Symmetrical.

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

// C program to check whether given matrix 
// is skew-symmetric or not 
#include <stdio.h> 
#include <stdlib.h> 
  
#define ROW 3 
#define COL 3 
  
// Utility function to create transpose matrix 
void transpose(int transpose_matrix[ROW][COL], 
                         int matrix[ROW][COL]) 
{ 
   for (int i = 0; i < ROW; i++) 
      for (int j = 0; j < COL; j++) 
         transpose_matrix[j][i] = matrix[i][j]; 
} 
  
// Utility function to check skew - symmetric 
// matrix condition 
bool check(int transpose_matrix[ROW][COL], 
                    int matrix[ROW][COL]) 
{ 
    for (int i = 0; i < ROW; i++) 
        for (int j = 0; j < COL; j++) 
            if (matrix[i][j] != -transpose_matrix[i][j]) 
                return false; 
    return true; 
} 
  
// Utility function to print a matrix 
void printMatrix(int matrix[ROW][COL]) 
{ 
    for (int i = 0; i < ROW; i++) 
    { 
       for (int j = 0; j < COL; j++) 
            printf("%d ", matrix[i][j]); 
       printf("\n"); 
    } 
} 
  
// Driver program to test above functions 
int main() 
{ 
    int matrix[ROW][COL] = { 
                            {0, 5, -4}, 
                            {-5, 0, 1}, 
                            {4, -1, 0}, 
                           }; 
  
    int transpose_matrix[ROW][COL]; 
  
    // Function create transpose matrix 
    transpose(transpose_matrix, matrix); 
  
    printf ("Transpose matrix: \n"); 
    printMatrix(transpose_matrix); 
  
    // Check whether matrix is skew-symmetric or not 
    if (check(transpose_matrix, matrix)) 
       printf("Skew Symmetric Matrix"); 
    else
       printf("Not Skew Symmetric Matrix"); 
  
    return 0; 
} 

Java

// java program to check 
// whether given matrix 
// is skew-symmetric or not 
import java.io.*; 
  
class GFG { 
      
static int ROW =3; 
static int COL =3; 
  
// Utility function to create transpose matrix 
 static void transpose(int transpose_matrix[][], 
                        int matrix[][]) 
{ 
for (int i = 0; i < ROW; i++) 
    for (int j = 0; j < COL; j++) 
        transpose_matrix[j][i] = matrix[i][j]; 
} 
  
// Utility function to check skew - symmetric 
// matrix condition 
 static boolean check(int transpose_matrix[][], 
                    int matrix[][]) 
{ 
    for (int i = 0; i < ROW; i++) 
        for (int j = 0; j < COL; j++) 
            if (matrix[i][j] != -transpose_matrix[i][j]) 
                return false; 
    return true; 
} 
  
// Utility function to print a matrix 
 static void printMatrix(int matrix[][]) 
{ 
    for (int i = 0; i < ROW; i++) 
    { 
    for (int j = 0; j < COL; j++) 
            System.out.print(matrix[i][j] + " "); 
    System.out.println(); 
    } 
} 
  
// Driver program to test above functions 
public static void main (String[] args) { 
        int matrix[][] = { 
                            {0, 5, -4}, 
                            {-5, 0, 1}, 
                            {4, -1, 0}, 
                        }; 
  
    int transpose_matrix[][] = new int[ROW][COL]; 
  
    // Function create transpose matrix 
    transpose(transpose_matrix, matrix); 
  
    System.out.println ("Transpose matrix: "); 
    printMatrix(transpose_matrix); 
  
    // Check whether matrix is skew-symmetric or not 
    if (check(transpose_matrix, matrix)) 
    System.out.println("Skew Symmetric Matrix"); 
    else
    System.out.println("Not Skew Symmetric Matrix"); 
  
          
    } 
} 
  
// This code is contributed by vt_m. 

Python3

# Python 3 program to check 
# whether given matrix 
# is skew-symmetric or not 
ROW=3
COL=3
  
# Utility function to 
# create transpose matrix 
def transpose(transpose_matrix,matrix): 
    for i in range (ROW): 
        for j in range(COL): 
            transpose_matrix[j][i] = matrix[i][j] 
              
# Utility function to 
# check skew - symmetric 
# matrix condition 
def check(transpose_matrix,matrix): 
    for i in range(ROW): 
        for j in range(COL): 
            if (matrix[i][j] != -transpose_matrix[i][j]): 
                return False
    return True
      
# Utility function to print a matrix 
def printMatrix(matrix): 
    for i in range (ROW): 
        for j in range(COL): 
            print(matrix[i][j]," ",end="") 
        print() 
          
# Driver program to test above functions 
matrix= [ 
            [0, 5, -4], 
            [-5, 0, 1], 
            [4, -1, 0], 
        ] 
transpose_matrix=[[0 for i in range(3)] for j in range(3)] 
  
# Function create transpose matrix 
transpose(transpose_matrix, matrix) 
print("Transpose matrix:") 
printMatrix(transpose_matrix) 
  
# Check whether matrix is 
# skew-symmetric or not 
if (check(transpose_matrix, matrix)): 
    print("Skew Symmetric Matrix") 
else: 
    print("Not Skew Symmetric Matrix") 
  
# This code is contributed 
# by Azkia Anam. 

C#

// C# program to check 
// whether given matrix 
// is skew-symmetric or not 
using System; 
  
class GFG  
{ 
static int ROW =3; 
static int COL =3; 
  
// Utility function to 
// create transpose matrix 
static void transpose(int [,]transpose_matrix, 
                      int [,]matrix) 
{ 
for (int i = 0; i < ROW; i++) 
    for (int j = 0; j < COL; j++) 
        transpose_matrix[j,i] = matrix[i,j]; 
} 
  
// Utility function to check  
// skew - symmetric matrix  
// condition 
static bool check(int [,]transpose_matrix, 
                  int [,]matrix) 
{ 
    for (int i = 0; i < ROW; i++) 
        for (int j = 0; j < COL; j++) 
            if (matrix[i, j] !=  
                -transpose_matrix[i, j]) 
                return false; 
    return true; 
} 
  
// Utility function 
// to print a matrix 
static void printMatrix(int [,]matrix) 
{ 
    for (int i = 0; i < ROW; i++) 
    { 
    for (int j = 0; j < COL; j++) 
            Console.Write(matrix[i, j] +  
                                   " "); 
    Console.WriteLine(); 
    } 
} 
  
// Driver Code 
public static void Main ()  
{ 
    int [,]matrix = {{0, 5, -4}, 
                     {-5, 0, 1}, 
                     {4, -1, 0},}; 
  
    int [,]transpose_matrix = new int[ROW, COL]; 
  
    // Function create transpose matrix 
    transpose(transpose_matrix, matrix); 
  
    Console.WriteLine("Transpose matrix: "); 
    printMatrix(transpose_matrix); 
  
    // Check whether matrix is 
    // skew-symmetric or not 
    if (check(transpose_matrix, matrix)) 
    Console.WriteLine("Skew Symmetric Matrix"); 
    else
    Console.WriteLine("Not Skew Symmetric Matrix"); 
    } 
} 
  
// This code is contributed by anuj_67. 

Output :

Transpose matrix: 
0 -5 4 
5 0 -1 
-4 1 0 
Skew Symmetric Matrix

References : Wikipedia

This article is contributed by Akash Gupta. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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My Personal Notes

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

C++

Java

Python3

C#

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