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: 6Input: 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 matrixint 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 codeint 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 approachimport java.io.*; class GFG{ static int N = 4; // Function to return the sum of eigen// values of the given matrixstatic 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 codepublic 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 matrixdef sumEigen(mat): sum = 0 # Calculate the sum of # the diagonal elements for i in range(N): sum += (mat[i][i]) return sum # Driver codemat= [ [ 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 approachusing System; class GFG{ static int N = 4; // Function to return the sum of eigen// values of the given matrixstatic 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 codestatic 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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