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Find the sum of Eigen Values of the given N*N matrix
  • Last Updated : 09 Jul, 2019

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++




// 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;
}


Java




// 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.. 


Python3




# 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


C#




// 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... 


Output:

34

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