Matrix: Given a matrix, check if it is skew symmetric or not

Problem Statement:

A matrix is called as skew symmetric matrix , whose transpose is negative of the original matrix.

i.e if the entry in ith row and jth column of matrix a[i][j] then the skew symmetric matrix will be -a[i][j]

Example:

Input matrix:


A[] [] = { { 0,  2, -3},
		   {-2,  0, 7},
		   { 3, -7, 0} };

Output:

Transpose of the matrix:

A[] [] = { { 0, -2, 3},
		   { 2,  0,-7},
		   {-3,  7, 0} };

Yes

Solution Explanation:

Solution is very simple.

First we need to find the transpose of the input matrix.

Then if the input matrix is equal to the -ve of its transpose matrix, then it is a skew symmetrical matrix.

Time Complexity: O( row * column )
Space Complexity: O( row * column )

Code Solution

#include <iostream>
#include <vector>
using namespace std;

#define row 3
#define col 3


void getTranspose(int transpose_result[row][col],
                         int matrix[row][col])
{
   for (int i = 0; i < row; i++)
      for (int j = 0; j < col; j++)
         transpose_result[j][i] = matrix[i][j];
}

bool checkIfSkewSymmentric(int transpose_result[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_result[i][j])
                return false;
    return true;
}

int main()
{
    int matrix[row][col] = { { 0,  2, -3},
		   					 {-2,  0,  7},
		   					 { 3, -7, 0} };

    int transpose_result[row][col];

    getTranspose(transpose_result, matrix);

    if (checkIfSkewSymmentric(transpose_result, matrix))
       cout<<"Matrix is a Skew Symmetric Matrix";
    else
       cout<<"Matrix is Not a Skew Symmetric Matrix";

    return 0;
}

Output

Matrix is a Skew Symmetric Matrix