#include <iostream>
#include <iomanip>
#include <armadillo>
using namespace std;
using namespace arma;
int main(){
  mat A = randu<mat>(5,5);  
  vec eigval;  
  mat eigvec;
  A = A+trans(A);  cout<< "A= \n"<<A<<endl;;

  eig_sym(eigval, eigvec, A);
   
  vec x(eigval);
  for (unsigned i=0;i<A.n_rows;i++){
    cout<<i<<"th eigenvalue = "<<eigval(i)<<endl;
    x = eigvec.col(i); //x(j) =  eigvec(j,i);  
    cout<<"               x = "<<trans(x);
    x = A*x/eigval(i);
    cout<<"check: Ax/lambda = "<<trans(x)<<endl;
  }
  return 0;
}