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

using namespace Eigen;
using namespace std;

int main() {
  MatrixXd A(2, 2);
  A << 1, 2,
       3, 4;
  MatrixXd B(2, 2);
  B << 5, 6,
       7, 8;

  // Matrix summation
  MatrixXd C = A + B;
  cout << "C = " << endl << C << endl;  // Output: C = 6 8
                                        //           10 12

  return 0;
}

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

using namespace Eigen;
using namespace std;

int main() {
  MatrixXd A(2, 2);
  A << 1, 2,
       3, 4;
  MatrixXd B(2, 2);
  B << 5, 6,
       7, 8;

  // Matrix subtraction
  MatrixXd C = A - B;
  cout << "C = " << endl << C << endl;  // Output: C = -4 -4
                                        //           -4 -4

  return 0;
}

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

using namespace Eigen;
using namespace std;

int main() {
  VectorXd a(2);
  a << 1, 2;
  VectorXd b(2);
  b << 3, 4;

  // Inner product
  double inner = a.dot(b);
  cout << "inner = " << inner << endl;  // Output: inner = 11

  return 0;
}

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

using namespace Eigen;
using namespace std;

int main() {
  Vector3d a(1, 2, 3);
  Vector3d b(4, 5, 6);

  // Cross product
  Vector3d c = a.cross(b);
  cout << "c = " << c << endl;  // Output: c = [-3, 6, -3]

  return 0;
}