# 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

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

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 ` `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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Improved By : mohit kumar 29, jit_t

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