Matrix is orthogonal or not

Posted on Apr 26, 2020

C program to check whether matrix is orthogonal or not.

An orthogonal matrix is a square matrix that satisfies the following condition:
A * A^T = I (Identity Matrix)

So, A Matrix is an orthogonal matrix, when we multiply it with its transpose, we get an identity matrix.

Program

#include<stdio.h>
#include<conio.h>
#define MAX 10

void read_matrix(int mat[MAX][MAX], int row, int col)
{
    int i, j;
    for(i=0;i<row;i++)
    {
        for(j=0;j<col;j++)
        {
            printf("Element [%d][%d]\t:",i,j);
            scanf("%d",&mat[i][j]);
        }
    }
}

void print_matrix(int mat[MAX][MAX], int row, int col)
{
    int i, j;
    for(i=0;i<row;i++)
    {
        for(j=0;j<col;j++)
        {
            printf("%d\t",mat[i][j]);
        }
        printf("\n");
    }
}

void transpose(int mat[MAX][MAX], int trans[MAX][MAX], int row)
{
    int i, j;

    for(i=0;i<row;i++)
    {
        for(j=0;j<row;j++)
        {
            trans[j][i] = mat[i][j];
        }
    }
}

void multiply(int mat[MAX][MAX], int trans[MAX][MAX], int mul[MAX][MAX], int row)
{
    int i, j, k;

    for(i=0;i<row;i++)
    {
        for(j=0;j<row;j++)
        {
            mul[i][j] = 0;
            for(k=0;k<row;k++)
            {
                mul[i][j] = mul[i][j] + (mat[i][k] * trans[k][j]);
            }
        }
    }
}

void identity(int mat[MAX][MAX], int row)
{
    int i, j, flag;

    flag = 0;
    for(i=0;i<row;i++)
    {
        for(j=0;j<row;j++)
        {
            if((i==j) && mat[i][j]!=1.0)
            {
                flag = 1;
            }
            else if(i!=j && mat[i][j]!=0.0)
            {
                flag = 1;
            }

        }
    }

    if(flag == 0)
    {
        printf("\nMatrix is orthogonal matrix");
    }
    else
    {
        printf("\nMatrix is not an orthogonal matrix");
    }
}

void orthogonal(int mat[MAX][MAX], int row)
{
    int i, j;
    int trans[MAX][MAX], mul[MAX][MAX];

    transpose(mat, trans, row);
    multiply(mat, trans, mul, row);
    identity(mul, row);
}

void main()
{
    int mat[MAX][MAX];
    int row, col;

    printf("Enter the number of rows or columns of the square matrix\t:");
    scanf("%d",&row);
    col = row;

    printf("Enter the elements of the matrix\n");
    read_matrix(mat, row, col);

    printf("\nMatrix entered is\n");
    print_matrix(mat, row, col);

    orthogonal(mat, row);

    getch();
}

Output

********** Run1 ********** 

Enter the number of rows or columns of the square matrix        :4
Enter the elements of the matrix
Element [0][0]  :0
Element [0][1]  :0
Element [0][2]  :0
Element [0][3]  :1
Element [1][0]  :0
Element [1][1]  :0
Element [1][2]  :1
Element [1][3]  :0
Element [2][0]  :1
Element [2][1]  :0
Element [2][2]  :0
Element [2][3]  :0
Element [3][0]  :0
Element [3][1]  :1
Element [3][2]  :0
Element [3][3]  :0

Matrix entered is
0       0       0       1
0       0       1       0
1       0       0       0
0       1       0       0

Matrix is orthogonal matrix


********** Run2 ********** 

Enter the number of rows or columns of the square matrix        :4
Enter the elements of the matrix
Element [0][0]  :1
Element [0][1]  :0
Element [0][2]  :0
Element [0][3]  :0
Element [1][0]  :0
Element [1][1]  :0
Element [1][2]  :1
Element [1][3]  :0
Element [2][0]  :0
Element [2][1]  :1
Element [2][2]  :0
Element [2][3]  :0
Element [3][0]  :0
Element [3][1]  :1
Element [3][2]  :0
Element [3][3]  :0

Matrix entered is
1       0       0       0
0       0       1       0
0       1       0       0
0       1       0       0

Matrix is not an orthogonal matrix