#include <Eigen/Dense>
#include <iostream>

using namespace Eigen;
using namespace std;
int main() {
  Vector3d v(1, 2, 3);
  Vector3d w(0, 1, 2);

  cout << "Dot product: " << v.dot(w) << endl;
  double dp =
      v.adjoint() * w;  // automatic conversion of the inner product to a scalar
  cout << "Dot product via a matrix product: " << dp << endl;
  cout << "Cross product:\n" << v.cross(w) << endl;
}