Find the sum of Eigen Values of the given N*N matrix

Given an N*N matrix mat[][], the task is to find the sum of Eigen values of the given matrix.

Examples:

Input: mat[][] = {
{2, -1, 0},
{-1, 2, -1},
{0, -1, 2}}
Output: 6



Input: mat[][] = {
{1, 2, 3, 4},
{5, 6, 7, 8},
{9, 10, 11, 12},
{13, 14, 15, 16}}
Output: 34

Approach: The sum of Eigen values of a matrix is equal to the trace of the matrix. The trace of an n × n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A.

Below is the implementation of the above approach:

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
#define N 4
  
// Function to return the sum of eigen
// values of the given matrix
int sumEigen(int mat[N][N])
{
    int sum = 0;
  
    // Calculate the sum of
    // the diagonal elements
    for (int i = 0; i < N; i++)
        sum += (mat[i][i]);
  
    return sum;
}
  
// Driver code
int main()
{
    int mat[N][N] = { { 1, 2, 3, 4 },
                      { 5, 6, 7, 8 },
                      { 9, 10, 11, 12 },
                      { 13, 14, 15, 16 } };
  
    cout << sumEigen(mat);
  
    return 0;
}

chevron_right






                        filter_none









Java














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// Java implementation of the approach 


import java.io.*; 


  


class GFG 


{ 


      


static int N = 4; 


  


// Function to return the sum of eigen 


// values of the given matrix 


static int sumEigen(int mat[][]) 


{ 


    int sum = 0; 


  


    // Calculate the sum of 


    // the diagonal elements 


    for (int i = 0; i < N; i++) 


        sum += (mat[i][i]); 


  


    return sum; 


} 


  


// Driver code 


public static void main (String[] args)  


{ 


  


    int mat[][] = { { 1, 2, 3, 4 }, 


                    { 5, 6, 7, 8 }, 


                    { 9, 10, 11, 12 }, 


                    { 13, 14, 15, 16 } }; 


  


    System.out.println (sumEigen(mat)); 


} 


} 


  


// The code is contributed by Tushil..  



















                        chevron_right







                        filter_none









Python3














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















# Python3 implementation of the approach 


  


N=4


  


# Function to return the sum of eigen 


# values of the given matrix 


def sumEigen(mat): 


  


    sum = 0


  


    # Calculate the sum of 


    # the diagonal elements 


    for i in range(N): 


        sum += (mat[i][i]) 


  


    return sum


  


  


# Driver code 


mat= [ [ 1, 2, 3, 4 ], 


    [ 5, 6, 7, 8 ], 


    [ 9, 10, 11, 12 ], 


    [ 13, 14, 15, 16 ] ] 


  


print(sumEigen(mat)) 


  


# This code is contributed by mohit kumar 29 



















                        chevron_right







                        filter_none









C#














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// C# implementation of the approach 


using System; 


  


class GFG 


{ 


          


static int N = 4; 


  


// Function to return the sum of eigen 


// values of the given matrix 


static int sumEigen(int [,]mat) 


{ 


    int sum = 0; 


  


    // Calculate the sum of 


    // the diagonal elements 


    for (int i = 0; i < N; i++) 


        sum += (mat[i,i]); 


  


    return sum; 


} 


  


// Driver code 


static public void Main () 


{ 


      


    int [,]mat = { { 1, 2, 3, 4 }, 


                    { 5, 6, 7, 8 }, 


                    { 9, 10, 11, 12 }, 


                    { 13, 14, 15, 16 } }; 


  


    Console.Write(sumEigen(mat)); 


} 


} 


  


// The code is contributed by ajit...  



















                        chevron_right







                        filter_none











Output:


34






          
          
          
          

            

    

        My Personal Notes
        arrow_drop_up
    

    

        
        

            
            
        

    


Recommended Posts:
gp6
Check out this Author's contributed articles.
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on  the "Improve Article" button below.


Improved By :  mohit kumar 29, jit_t


      
      
      
      

      

      
					
		

    Article Tags : 
Matrix

           	
Practice Tags : 
Matrix

        

         

         
 
         
        Be the First to upvote.

                

        



        
        
        
        
        

    

            

            0
            

            

                             No votes yet.
                    

            
            
            
            
            
        

        
        

        

        

        

        

        

        


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.