#include <iostream>
#include <iomanip>
#include <math.h>
using namespace std;
int main() {
// Define the matrix.
double A[3][3] = {
{1, 2, 3},
{4, 5, 6},
{7, 8, 9}
};
// Find the eigenvalues and eigenvectors.
double eigenvalues[3];
double eigenvectors[3][3];
bool foundEigenvectors = false;
for (int i = 0; i < 3; i++) {
double a = A[i][i] - eigenvalues[0];
double b = A[i][i] - eigenvalues[1];
double c = A[i][i] - eigenvalues[2];
double d = A[i][0] + A[i][1] + A[i][2];
double e = A[0][0] * A[1][1] + A[0][0] * A[2][2] + A[1][1] * A[2][2] - A[0][1] * A[0][1] - A[0][2] * A[0][2] - A[1][2] * A[1][2];
double det = a * b * c - d * e;
if (det != 0) {
eigenvalues[i] = det / (a * b - d * c);
double x1 = (b * e - d * c) / (a * b - d * c);
double x2 = (a * e - d * b) / (a * b - d * c);
eigenvectors[i][0] = x1;
eigenvectors[i][1] = x2;
eigenvectors[i][2] = 1 - x1 - x2;
foundEigenvectors = true;
}
}
// Print the eigenvalues and eigenvectors.
if (foundEigenvectors) {
cout << "Eigenvalues: " << endl;
for (int i = 0; i < 3; i++) {
cout << eigenvalues[i] << " ";
}
cout << endl;
cout << "Eigenvectors: " << endl;
for (int i = 0; i < 3; i++) {
cout << setprecision(3) << eigenvectors[i][0] << " " << eigenvectors[i][1] << " " << eigenvectors[i][2] << endl;
}
} else {
cout << "No eigenvalues found." << endl;
}
return 0;
}
