Normal and Trace of a Matrix in Java

Normal of a matrix

The square root of the total squares of each element in a matrix is known as the matrix's normal. Think of the following matrix as an example.

Example:

[[1,2,3]

  [4,5,6]

  [7,8,9]]

sumofSqures=1*1+2*2+3*3+4*4+5*5+6*6+7*7+8*8+9*9=

sumofSqures=385

Now find the square root of the number of sumofSqures.

Normal=sqrt(385)

Normal=16.8

A Matrix trace

All the components that make up a matrix's major diagonal are added to form the trace (upper left to lower right). You should be aware that matrices must be square (Matrix should consist of an equal number of rows and columns). Solutions in linear algebra are useful to prove.

[[1,2,3]

  [4,5,6]

  [7,8,9]]

TraceofMatrix=1+5+9

TraceofMatrix=15

Java Program for normal and a trace of the matrix

NormalandTrace.java

//this program is for finding the normal and the trace of the matrix
//importing the packages required
import java.util.*;  
public class NormalandTrace  
{  
    public static void main(String args[])  
    {  
        int arr[][] = new int[5][5];  
        int i, j;  
        double total = 0, sq = 0, res = 0;  
    Scanner sc = new Scanner(System.in);  
    System.out.print("Please enter the num of rows: ");  
    // reading the integer value as rows from the user 
    int r= sc.nextInt();  
    System.out.print("Please enter the num of columns: ");  
    // reading the integer value as columns from the user
    int c = sc.nextInt();  
    System.out.println("Enter matrix:");  
    //loop for iterating the rows 
    for(i = 0; i < r; i++)  
    {  
        //loop for iterating columns  
        for(j = 0; j < c; j++)   
            {  
                //reading the elements in the matrix   
                arr[i][j] = sc.nextInt();  
                // the space is printed  
                System.out.print(" ");  
            }  
        }  
    System.out.println("Displaying the entered matrix: ");  
    // displaying the entered integers as the matrix
    for(i = 0; i < r; i++)  
        {  
            for(j = 0; j < c; j++)  
            {  
            System.out.print(arr[i][j]+" ");  
            }  
            System.out.println(" ");  
        }  
        System.out.println("Displaying the trace of the matrix:");
    for(i = 0; i < r; i++)  
    {    
            for(j = 0; j < c; j++)  
            {  
                //the condition for checking the element has i==j 
                if(i == j)  
                 {  
                     // the sum of the elements of the principal diagonal  
                     total = total + (arr[i][j]);  
                 }  
            }  
        }  
        //printing the trace of the matrix  
        System.out.println(total);    
        System.out.println("The result of the normal is: ");   
          
    for(i = 0; i < r; i++)  
    {  
            for(j = 0; j < c; j++)  
            {  
                //th sum of the squares of the elements in the matrix   
                sq = sq + (arr[i][j])*(arr[i][j]);  
            }  
        }  
        // finding the square root of the number(sq) 
        res = Math.sqrt(sq);  
        // printing the result as the normal of the matrix 
        System.out.println(res);  
    }  
}  

Output

Please enter the num of rows: 3
Please enter the num of columns: 3
Enter matrix:
1 
2
 3
 4
 5
 6
 7
 8
 9
 Displaying the entered matrix: 
1 2 3  
4 5 6  
7 8 9  
Displaying the trace of the matrix:
15.0
The result of the normal is: 
16.881943016134134

NormalTrace2.java

//this program is for finding the normal and the trace of the matrix
//importing the packages required
import java.io.*;  
public class NormalTrace2  
{  
// declaring the maximum size of the matrix
static int MAX = 10;  
// the method can calculate and return the normal of the matrix 
static int findNormal(int m[][], int num)  
{  
    //storing the sumofsquares in the total variable
    int total = 0;  
    for (int i=0; i<num; i++)  
        for (int j=0; j<num; j++)  
            total = total + m[i][j]*m[i][j];  
    return (int)Math.sqrt(total);  
}  
// method for finding the trace of the matrix
static int findTrace(int m[][], int num)  
{  
    //storing the result in total variable
    int total = 0;  
    for (int i=0; i<num; i++)  
        total = total + m[i][i];  
    return total;  
}  
//main section of the program  
public static void main (String args[])   
    {  
        // static way of representing elements in the matrix
        int m[][] = {{5, 3, 24, 1, 45},  
                          {27, 8, 33, 15, 9},  
                          {1, 11, 10, 5, 5},  
                          {45, 18, 3, 9, 14},  
                          {19, 3, 3, 13, 4},  
                         };  
        //printing the normal and trace of the matrix m[][]
        
        System.out.println ("The Trace for the given matrix is: "+ findTrace(m, 5));  
        System.out.println ("The result of Normal is: "+ findNormal(m, 5));  
    }  
}  

Output

The Trace for the given matrix is: 36
The result of Normal is: 91