what is use of eigenvalue and eigenvector code example

Example: eigenvalue of matrix c++ using Eigen

#include <eigen3/Eigen/Eigenvalues> // header file
  #include <iostream>

  int main(){
  Eigen::Matrix<double, 2, 2> A; // declare a real (double) 2x2 matrix
  A << 0, 2, 1, 0; // defined the matrix A

  Eigen::EigenSolver<Eigen::Matrix<double, 2,2> > s(A); // the instance s(A) includes the eigensystem
  std::cout << A << std::endl;
  std::cout << "eigenvalues:" << std::endl;
  std::cout << s.eigenvalues()(0) << std::endl;
  std::cout << "eigenvectors=" << std::endl;
  std::cout << s.eigenvectors() << std::endl;

  return(0);
}