Encuentre la suma de los valores propios de la array N*N dada

Dada una array N*N mat[][] , la tarea es encontrar la suma de los valores propios de la array dada.
Ejemplos: 
 

Entrada: mat[][] = { 
{2, -1, 0}, 
{-1, 2, -1}, 
{0, -1, 2}} 
Salida: 6
Entrada: mat[][] = { 
{ 1, 2, 3, 4}, 
{5, 6, 7, 8}, 
{9, 10, 11, 12}, 
{13, 14, 15, 16}} 
Salida: 34 
 

Enfoque: La suma de los valores propios de una array es igual a la traza de la array. La traza de una array cuadrada A n × n se define como la suma de los elementos en la diagonal principal (la diagonal desde la esquina superior izquierda hasta la esquina inferior derecha) de A.
A continuación se muestra la implementación del enfoque anterior: 
 

// 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 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 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# 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...

<script>
 
// Javascript implementation of the approach
var N = 4;
 
// Function to return the sum of eigen
// values of the given matrix
function sumEigen(mat)
{
    var sum = 0;
 
    // Calculate the sum of
    // the diagonal elements
    for (var i = 0; i < N; i++)
        sum += (mat[i][i]);
 
    return sum;
}
 
// Driver code
var mat = [ [ 1, 2, 3, 4 ],
                  [ 5, 6, 7, 8 ],
                  [ 9, 10, 11, 12 ],
                  [ 13, 14, 15, 16 ] ];
document.write( sumEigen(mat));
 
</script>

34