diff --git a/cpp/kiss_icp/core/Registration.cpp b/cpp/kiss_icp/core/Registration.cpp
index c3e0d49c..1d22bef0 100644
--- a/cpp/kiss_icp/core/Registration.cpp
+++ b/cpp/kiss_icp/core/Registration.cpp
@@ -32,7 +32,9 @@
 #include <tuple>
 
 namespace Eigen {
+using Matrix6d = Eigen::Matrix<double, 6, 6>;
 using Matrix3_6d = Eigen::Matrix<double, 3, 6>;
+using Vector6d = Eigen::Matrix<double, 6, 1>;
 }  // namespace Eigen
 
 namespace {
@@ -63,10 +65,6 @@ void TransformPoints(const Sophus::SE3d &T, std::vector<Eigen::Vector3d> &points
 constexpr int MAX_NUM_ITERATIONS_ = 500;
 constexpr double ESTIMATION_THRESHOLD_ = 0.0001;
 
-}  // namespace
-
-namespace kiss_icp {
-
 std::tuple<Eigen::Matrix6d, Eigen::Vector6d> BuildLinearSystem(
     const std::vector<Eigen::Vector3d> &source,
     const std::vector<Eigen::Vector3d> &target,
@@ -103,6 +101,9 @@ std::tuple<Eigen::Matrix6d, Eigen::Vector6d> BuildLinearSystem(
 
     return std::make_tuple(JTJ, JTr);
 }
+}  // namespace
+
+namespace kiss_icp {
 
 Sophus::SE3d RegisterFrame(const std::vector<Eigen::Vector3d> &frame,
                            const VoxelHashMap &voxel_map,
diff --git a/cpp/kiss_icp/core/Registration.hpp b/cpp/kiss_icp/core/Registration.hpp
index 05d1dc99..eb82d37b 100644
--- a/cpp/kiss_icp/core/Registration.hpp
+++ b/cpp/kiss_icp/core/Registration.hpp
@@ -28,18 +28,8 @@
 
 #include "VoxelHashMap.hpp"
 
-namespace Eigen {
-using Matrix6d = Eigen::Matrix<double, 6, 6>;
-using Vector6d = Eigen::Matrix<double, 6, 1>;
-}  // namespace Eigen
-
 namespace kiss_icp {
 
-std::tuple<Eigen::Matrix6d, Eigen::Vector6d> BuildLinearSystem(
-    const std::vector<Eigen::Vector3d> &source,
-    const std::vector<Eigen::Vector3d> &target,
-    double kernel);
-
 Sophus::SE3d RegisterFrame(const std::vector<Eigen::Vector3d> &frame,
                            const VoxelHashMap &voxel_map,
                            const Sophus::SE3d &initial_guess,