求给定 N*N 矩阵的特征值之和

给定一个N*N矩阵mat[][] ，任务是找到给定矩阵的特征值之和。
例子：

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

编程需要懂一点英语

方法：矩阵的特征值之和等于矩阵的迹。 n × n 方阵 A 的迹定义为 A 的主对角线（从左上角到右下角的对角线）上元素之和。
下面是上述方法的实现：

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...

Javascript

输出：