Program to find Normal and Trace of a matrix

Given a 2D matrix, the task is to find Trace and Normal of matrix.

Normal of a matrix is defined as square root of sum of squares of matrix elements.

Trace of a n x n square matrix is sum of diagonal elements.

Examples :

Input : mat[][] = {{7, 8, 9},
                   {6, 1, 2},
                   {5, 4, 3}};
Output : Normal = 16  
         Trace  = 11
Explanation : 
Normal = sqrt(7*7+ 8*8 + 9*9 + 6*6 +
              1*1 + 2*2 + 5*5 + 4*4 + 3*3)   
       = 16
Trace  = 7+1+3 = 11

Input :mat[][] = {{1, 2, 3},
                  {6, 4, 5},
                  {2, 1, 3}};
Output : Normal = 10  
         Trace = 8
Explanation : 
Normal = sqrt(1*1 +2*2 + 3*3 + 6*6 + 4*4 + 
             5*5 + 2*2 + 1*1 + 3*3)   
Trace = 8(1+4+3)

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

Untitled

C++

// C++ program to find trace and normal 
// of given matrix 
#include<bits/stdc++.h> 
using namespace std; 
  
// Size of given matrix 
const int MAX = 100; 
  
// Returns Normal of a matrix of size n x n 
int findNormal(int mat[][MAX], int n) 
{ 
    int sum = 0; 
    for (int i=0; i<n; i++) 
        for (int j=0; j<n; j++) 
            sum += mat[i][j]*mat[i][j]; 
    return sqrt(sum); 
} 
  
// Returns trace of a matrix of size n x n 
int findTrace(int mat[][MAX], int n) 
{ 
    int sum = 0; 
    for (int i=0; i<n; i++) 
         sum += mat[i][i]; 
    return sum; 
} 
  
// Driven source 
int main() 
{ 
    int mat[][MAX] = {{1, 1, 1, 1, 1}, 
        {2, 2, 2, 2, 2}, 
        {3, 3, 3, 3, 3}, 
        {4, 4, 4, 4, 4}, 
        {5, 5, 5, 5, 5}, 
    }; 
    cout << "Trace of Matrix = "
         << findTrace(mat, 5) << endl; 
    cout << "Normal of Matrix = "
         << findNormal(mat, 5) << endl; 
    return 0; 
} 

Java

// Java program to find trace and normal 
// of given matrix 
  
import java.io.*; 
  
class GFG { 
  
// Size of given matrix 
static  int MAX = 100; 
  
// Returns Normal of a matrix of size n x n 
 static int findNormal(int mat[][], int n) 
{ 
    int sum = 0; 
    for (int i=0; i<n; i++) 
        for (int j=0; j<n; j++) 
            sum += mat[i][j]*mat[i][j]; 
    return (int)Math.sqrt(sum); 
} 
  
// Returns trace of a matrix of size n x n 
 static int findTrace(int mat[][], int n) 
{ 
    int sum = 0; 
    for (int i=0; i<n; i++) 
        sum += mat[i][i]; 
    return sum; 
} 
  
// Driven source 
public static void main (String[] args) { 
  
            int mat[][] = {{1, 1, 1, 1, 1}, 
        {2, 2, 2, 2, 2}, 
        {3, 3, 3, 3, 3}, 
        {4, 4, 4, 4, 4}, 
        {5, 5, 5, 5, 5}, 
    }; 
  
    System.out.println ("Trace of Matrix = "
         + findTrace(mat, 5)); 
    System.out.println ("Normal of Matrix = "
         + findNormal(mat, 5)); 
          
    } 
}  
  
// This code is contributed by vt_m. 

Python3

# Python3 program to find trace and  
# normal of given matrix  
import math 
  
# Size of given matrix  
MAX = 100;  
  
# Returns Normal of a matrix  
# of size n x n  
def findNormal(mat, n):  
  
    sum = 0;  
    for i in range(n):  
        for j in range(n):  
            sum += mat[i][j] * mat[i][j];  
    return math.floor(math.sqrt(sum));  
  
# Returns trace of a matrix of  
# size n x n  
def findTrace(mat, n):  
  
    sum = 0;  
    for i in range(n):  
        sum += mat[i][i];  
    return sum;  
  
# Driver Code  
mat = [[1, 1, 1, 1, 1],  
       [2, 2, 2, 2, 2],  
       [3, 3, 3, 3, 3],  
       [4, 4, 4, 4, 4],  
       [5, 5, 5, 5, 5]];  
  
print("Trace of Matrix =", findTrace(mat, 5));  
  
print("Normal of Matrix =", findNormal(mat, 5));  
  
# This code is contributed by mits 

C#

// C# program to find trace and normal 
// of given matrix 
using System; 
  
class GFG { 
      
    // Returns Normal of a matrix of 
    // size n x n 
    static int findNormal(int [,]mat, int n) 
    { 
        int sum = 0; 
          
        for (int i = 0; i < n; i++) 
            for (int j = 0; j < n; j++) 
                sum += mat[i,j] * mat[i,j]; 
                  
        return (int)Math.Sqrt(sum); 
    } 
      
    // Returns trace of a matrix of size  
    // n x n 
    static int findTrace(int [,]mat, int n) 
    { 
        int sum = 0; 
          
        for (int i = 0; i < n; i++) 
            sum += mat[i,i]; 
              
        return sum; 
    } 
      
    // Driven source 
    public static void Main ()  
    { 
        int [,]mat = { {1, 1, 1, 1, 1}, 
                       {2, 2, 2, 2, 2}, 
                       {3, 3, 3, 3, 3}, 
                       {4, 4, 4, 4, 4}, 
                       {5, 5, 5, 5, 5}, 
    }; 
  
    Console.Write ("Trace of Matrix = "
            + findTrace(mat, 5) + "\n"); 
    Console.Write("Normal of Matrix = "
                    + findNormal(mat, 5)); 
          
    } 
}  
  
// This code is contributed by nitin mittal. 

PHP

<?php 
// PHP program to find trace and  
// normal of given matrix 
  
// Size of given matrix 
$MAX = 100; 
  
// Returns Normal of a  
// matrix of size n x n 
function findNormal($mat, $n) 
{ 
    $sum = 0; 
    for ( $i = 0; $i < $n; $i++) 
        for ( $j = 0; $j < $n; $j++) 
            $sum += $mat[$i][$j] *  
                    $mat[$i][$j]; 
    return floor(sqrt($sum)); 
} 
  
// Returns trace of a 
// matrix of size n x n 
function findTrace( $mat, $n) 
{ 
    $sum = 0; 
    for ( $i = 0; $i < $n; $i++) 
        $sum += $mat[$i][$i]; 
    return $sum; 
} 
  
// Driver Code 
$mat = array(array(1, 1, 1, 1, 1), 
             array(2, 2, 2, 2, 2), 
             array(3, 3, 3, 3, 3), 
             array(4, 4, 4, 4, 4), 
             array(5, 5, 5, 5, 5)); 
  
echo "Trace of Matrix = ",  
  findTrace($mat, 5),"\n"; 
  
echo "Normal of Matrix = " ,  
       findNormal($mat, 5) ; 
  
// This code is contributed by anuj_67. 
?> 

Output :

Trace of matrix = 15
Normal of matrix = 16

Time Complexity : O(n*n)
Space Complexity : O(1)

References:
https://en.wikipedia.org/wiki/Trace_(linear_algebra)

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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#

PHP

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