Question

Program to check whether the matrix is an orthogonal matrix
(To determine if a matrix is orthogonal, we need to multiply the matrix by it’s transpose, and see if we get the identity matrix.)

				
					Matrix:
[1,0,0]
[0,1,0]
[0,0,1]

TRANSPOSE:
[1,0,0]
[0,1,0]
[0,0,1]
PRODUCT OF TRANSPOSE MATRIX AND ORIGINAL MATRIX:
[1,0,0]
[0,1,0]
[0,0,1]
MATRIX IS ORTHOGONAL MATRIX

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Code

				
					import java.util.Scanner;
public class OrthogonalMatrix  
{  
    public static void main(String[] args)
    {  
        int row=0, col=0,i=0,j=0,k=0,sum=0;  
        int a[][],t[][],product[][];
        boolean flag=true;
        
        Scanner sc=new Scanner(System.in);
        System.out.println("ENTER THE ROW OF MATRIX");
        row=sc.nextInt();
        System.out.println("ENTER THE COLUMN OF MATRIX");
        col=sc.nextInt();
        if(row!=col)
        {
            System.out.println("MATRIX FIRST NEED TO BE SQUARE MATRIX");
        }
        else
        {
            a=new int[row][col];
            t=new int[row][col];
            System.out.println("ENTER THE ELEMENTS IN MATRIX");
            for(i=0;i< row;i++)
            {
                for(j=0;j< col;j++)
                {
                    a[i][j]=sc.nextInt();
                }
            }
            
            /*transpose of matrix starts here*/
            for(i=0;i< row;i++)
            {
                for(j=0;j< col;j++)
                {
                    t[i][j]=a[j][i];
                    
                }
            
            }
            /*transpose of matrix ends here*/
            
            /*printing of transpose matrix starts here*/
            System.out.println("Transpose of a matrix");
            
            for (i = 0; i < row; i++)  
            { 
                for (j = 0; j < col; j++)  
                { 
          
                    System.out.print(t[i][j]+" ");
                } 
                System.out.println();
            }
            /*printing of transpose matrix ends here*/
            
            /*product  of original matrix and transpose matrix starts here*/
            product=new int[row][col];
            for (i = 0; i < row; i++)  
            { 
                for (j = 0; j < col; j++)  
                { 
          
                    sum = 0; 
                    for (k = 0; k < row; k++)  
                    { 
                    
                        sum = sum + (a[i][k] * t[k][j]); 
                    } 
              
                    product[i][j] = sum; 
                } 
            } 
            /*product  of original matrix and transpose matrix ends here*/
            
            System.out.println("Product  of original matrix and transpose of original matrix matrix");
            
            for (i = 0; i < row; i++)  
            { 
                for (j = 0; j < col; j++)  
                { 
          
                    System.out.print(product[i][j]+" ");
                } 
                System.out.println();
            }
        
            /*checking whether the product is identity matrix.In identity matrix, all elements except on principal diagonal are zero and elements on principal diagonal are 1*/
            
            for(i=0;i< row;i++)
            {
                for(j=0;j< col;j++)
                {
                    if((i==j) &&product[i][j]!=1)
                    {
                        flag=false;
                        break;
                    }
                    if(i!=j && product[i][j]!=0)
                    {
                        flag=false;
                        break;
                    }
                }

            }
        
            if(flag==false)
            {
                System.out.println("MATRIX IS NOT ORTHOGONAL MATRIX");
            }
            else
            {
                System.out.println("MATRIX IS AN ORTHOGONAL MATRIX");
            }

       } 
        
    }  
}