diff --git a/Bounding_volumes/include/CGAL/Approximate_min_ellipsoid_d/Approximate_min_ellipsoid_d_impl.h b/Bounding_volumes/include/CGAL/Approximate_min_ellipsoid_d/Approximate_min_ellipsoid_d_impl.h
index 9c55b1bb92b..f740211bf95 100644
--- a/Bounding_volumes/include/CGAL/Approximate_min_ellipsoid_d/Approximate_min_ellipsoid_d_impl.h
+++ b/Bounding_volumes/include/CGAL/Approximate_min_ellipsoid_d/Approximate_min_ellipsoid_d_impl.h
@@ -20,9 +20,9 @@
 
 
 #ifdef CGAL_EIGEN3_ENABLED
-#include <CGAL/Eigen_vcm_traits.h>
+#include <CGAL/Eigen_diagonalize_traits.h>
 #else
-#include <CGAL/Internal_vcm_traits.h>
+#include <CGAL/Internal_diagonalize_traits.h>
 #endif
 
 #include <CGAL/Approximate_min_ellipsoid_d.h>
@@ -162,10 +162,10 @@ namespace CGAL {
     CGAL::cpp11::array<double, 2> eigenvalues;  // Note: sorted ascendent.
 
 #ifdef CGAL_EIGEN3_ENABLED
-    CGAL::Eigen_vcm_traits<double, 2>::diagonalize_selfadjoint_covariance_matrix
+    CGAL::Eigen_diagonalize_traits<double, 2>::diagonalize_selfadjoint_covariance_matrix
       (matrix, eigenvalues, eigenvectors);
 #else
-    CGAL::Internal_vcm_traits<double, 2>::diagonalize_selfadjoint_covariance_matrix
+    CGAL::Internal_diagonalize_traits<double, 2>::diagonalize_selfadjoint_covariance_matrix
       (matrix, eigenvalues, eigenvectors);
 #endif
     
@@ -209,10 +209,10 @@ namespace CGAL {
     CGAL::cpp11::array<double, 9> eigenvectors; // Note: not necessarily normalized.
     CGAL::cpp11::array<double, 3> eigenvalues;  // Note: sorted ascendent.
 #ifdef CGAL_EIGEN3_ENABLED
-    CGAL::Eigen_vcm_traits<double, 3>::diagonalize_selfadjoint_covariance_matrix
+    CGAL::Eigen_diagonalize_traits<double, 3>::diagonalize_selfadjoint_covariance_matrix
       (matrix, eigenvalues, eigenvectors);
 #else
-    CGAL::Internal_vcm_traits<double, 3>::diagonalize_selfadjoint_covariance_matrix
+    CGAL::Internal_diagonalize_traits<double, 3>::diagonalize_selfadjoint_covariance_matrix
       (matrix, eigenvalues, eigenvectors);
 #endif
     
diff --git a/Point_set_processing_3/include/CGAL/vcm_estimate_edges.h b/Point_set_processing_3/include/CGAL/vcm_estimate_edges.h
index f42bf2c3e2d..09207f859da 100644
--- a/Point_set_processing_3/include/CGAL/vcm_estimate_edges.h
+++ b/Point_set_processing_3/include/CGAL/vcm_estimate_edges.h
@@ -39,8 +39,8 @@ namespace CGAL {
 /// which however would result in selecting more points on sharper regions.
 /// More details are provided in \cgalCite{cgal:mog-vbcfe-11}.
 ///
-/// \tparam VCM_traits is a model of `VCMTraits`. If Eigen 3 (or greater) is available and `CGAL_EIGEN3_ENABLED` is defined
-///         then an overload using `Eigen_vcm_traits` is provided and this template parameter can be omitted.
+/// \tparam VCM_traits is a model of `DiagonalizeTraits`. If Eigen 3 (or greater) is available and `CGAL_EIGEN3_ENABLED` is defined
+///         then an overload using `Eigen_diagonalize_traits` is provided and this template parameter can be omitted.
 /// \sa CGAL::compute_vcm()`
 ///
 template <class FT, class VCM_traits>
@@ -73,9 +73,9 @@ vcm_is_on_feature_edge (cpp11::array<FT,6> &cov,
 {
   return vcm_is_on_feature_edge(cov, threshold,
 #ifdef CGAL_EIGEN3_ENABLED
-				CGAL::Eigen_vcm_traits<double, 3>()
+				CGAL::Eigen_diagonalize_traits<double, 3>()
 #else
-				CGAL::Internal_vcm_traits<double, 3>()
+				CGAL::Internal_diagonalize_traits<double, 3>()
 #endif
 				);
 
diff --git a/Point_set_processing_3/include/CGAL/vcm_estimate_normals.h b/Point_set_processing_3/include/CGAL/vcm_estimate_normals.h
index bb02a0b3205..7d41976f540 100644
--- a/Point_set_processing_3/include/CGAL/vcm_estimate_normals.h
+++ b/Point_set_processing_3/include/CGAL/vcm_estimate_normals.h
@@ -33,9 +33,9 @@
 #include <CGAL/Fuzzy_sphere.h>
 
 #ifdef CGAL_EIGEN3_ENABLED
-#include <CGAL/Eigen_vcm_traits.h>
+#include <CGAL/Eigen_diagonalize_traits.h>
 #else
-#include <CGAL/Internal_vcm_traits.h>
+#include <CGAL/Internal_diagonalize_traits.h>
 #endif
 
 #include <iterator>
@@ -370,8 +370,8 @@ vcm_estimate_normals (ForwardIterator first, ///< iterator over the first input
 /// @tparam ForwardIterator iterator over input points.
 /// @tparam PointPMap is a model of `ReadablePropertyMap` with a value_type = `Kernel::Point_3`.
 /// @tparam NormalPMap is a model of `WritablePropertyMap` with a value_type = `Kernel::Vector_3`.
-/// \tparam VCM_traits is a model of `VCMTraits`. If Eigen 3 (or greater) is available and `CGAL_EIGEN3_ENABLED` is defined
-///         then an overload using `Eigen_vcm_traits` is provided and this template parameter can be omitted.
+/// \tparam VCM_traits is a model of `DiagonalizeTraits`. If Eigen 3 (or greater) is available and `CGAL_EIGEN3_ENABLED` is defined
+///         then an overload using `Eigen_diagonalize_traits` is provided and this template parameter can be omitted.
 
 // This variant deduces the kernel from the point property map
 // and uses a radius for the convolution.
@@ -411,8 +411,8 @@ vcm_estimate_normals (ForwardIterator first, ///< iterator over the first input
 /// @tparam ForwardIterator iterator over input points.
 /// @tparam PointPMap is a model of `ReadablePropertyMap` with a value_type = `Kernel::Point_3`.
 /// @tparam NormalPMap is a model of `WritablePropertyMap` with a value_type = `Kernel::Vector_3`.
-/// \tparam VCM_traits is a model of `VCMTraits`. If Eigen 3 (or greater) is available and `CGAL_EIGEN3_ENABLED` is defined
-///         then an overload using `Eigen_vcm_traits` is provided and this template parameter can be omitted.
+/// \tparam VCM_traits is a model of `DiagonalizeTraits`. If Eigen 3 (or greater) is available and `CGAL_EIGEN3_ENABLED` is defined
+///         then an overload using `Eigen_diagonalize_traits` is provided and this template parameter can be omitted.
 
 // This variant deduces the kernel from the point property map
 // and uses a number of neighbors for the convolution.
@@ -456,9 +456,9 @@ vcm_estimate_normals (ForwardIterator first,
 {
   vcm_estimate_normals(first, beyond, point_pmap, normal_pmap, offset_radius, convolution_radius,
 #ifdef CGAL_EIGEN3_ENABLED
-		       CGAL::Eigen_vcm_traits<double, 3>()
+		       CGAL::Eigen_diagonalize_traits<double, 3>()
 #else
-		       CGAL::Internal_vcm_traits<double, 3>()
+		       CGAL::Internal_diagonalize_traits<double, 3>()
 #endif
 		       );
 }
@@ -477,9 +477,9 @@ vcm_estimate_normals (ForwardIterator first,
 {
   vcm_estimate_normals(first, beyond, point_pmap, normal_pmap, offset_radius, nb_neighbors_convolve,
 #ifdef CGAL_EIGEN3_ENABLED
-		       CGAL::Eigen_vcm_traits<double, 3>()
+		       CGAL::Eigen_diagonalize_traits<double, 3>()
 #else
-		       CGAL::Internal_vcm_traits<double, 3>()
+		       CGAL::Internal_diagonalize_traits<double, 3>()
 #endif
 		       );
 
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h
index c2cdea69c5c..30b28a9e1eb 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_2.h
@@ -29,10 +29,10 @@
 #include <CGAL/linear_least_squares_fitting_circles_2.h>
 #include <CGAL/linear_least_squares_fitting_rectangles_2.h>
 #include <CGAL/Dimension.h>
-#include <CGAL/Internal_vcm_traits.h>
+#include <CGAL/Internal_diagonalize_traits.h>
 
 #ifdef CGAL_EIGEN3_ENABLED
-#include <CGAL/Eigen_vcm_traits.h>
+#include <CGAL/Eigen_diagonalize_traits.h>
 #endif
 
 #include <iterator>
@@ -42,7 +42,7 @@ namespace CGAL {
 template < typename InputIterator, 
            typename Kernel,
 	   typename Tag,
-	   typename Vcm_traits>
+	   typename Diagonalize_traits>
 inline
 typename Kernel::FT
 linear_least_squares_fitting_2(InputIterator first,
@@ -51,16 +51,16 @@ linear_least_squares_fitting_2(InputIterator first,
                                typename Kernel::Point_2& centroid,
                                const Tag& tag,
 			       const Kernel& kernel,
-			       const Vcm_traits vcm_traits)
+			       const Diagonalize_traits diagonalize_traits)
 {
   typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
   return internal::linear_least_squares_fitting_2(first, beyond, line,
 						  centroid,(Value_type*)NULL,kernel,tag,
-						  vcm_traits);
+						  diagonalize_traits);
 }
 
 // deduces the kernel from the points in container.
-// Use default Vcm_traits
+// Use default Diagonalize_traits
 template < typename InputIterator, 
            typename Line,
            typename Point,
@@ -78,9 +78,9 @@ linear_least_squares_fitting_2(InputIterator first,
   return CGAL::linear_least_squares_fitting_2
     (first,beyond,line,centroid,tag,Kernel(),
 #ifdef CGAL_EIGEN3_ENABLED
-     Eigen_vcm_traits<typename Kernel::FT, 2>()
+     Eigen_diagonalize_traits<typename Kernel::FT, 2>()
 #else
-     Internal_vcm_traits<typename Kernel::FT, 2>()
+     Internal_diagonalize_traits<typename Kernel::FT, 2>()
 #endif
      );
 }
@@ -100,9 +100,9 @@ linear_least_squares_fitting_2(InputIterator first,
   typename Kernel::Point_2 centroid; // unused
   return CGAL::linear_least_squares_fitting_2(first,beyond,line,centroid,tag,Kernel(),
 #ifdef CGAL_EIGEN3_ENABLED
-     Eigen_vcm_traits<typename Kernel::FT, 2>()
+     Eigen_diagonalize_traits<typename Kernel::FT, 2>()
 #else
-     Internal_vcm_traits<typename Kernel::FT, 2>()
+     Internal_diagonalize_traits<typename Kernel::FT, 2>()
 #endif
      );
 }
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h
index b842bfc2b68..37f33fa180c 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_3.h
@@ -29,9 +29,9 @@
 #include <CGAL/linear_least_squares_fitting_tetrahedra_3.h>
 #include <CGAL/linear_least_squares_fitting_spheres_3.h>
 
-#include <CGAL/Internal_vcm_traits.h>
+#include <CGAL/Internal_diagonalize_traits.h>
 #ifdef CGAL_EIGEN3_ENABLED
-#include <CGAL/Eigen_vcm_traits.h>
+#include <CGAL/Eigen_diagonalize_traits.h>
 #endif
 
 #include <CGAL/Dimension.h>
@@ -46,7 +46,7 @@ template < typename InputIterator,
            typename Object,
            typename Kernel,
            typename Tag,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 inline
 typename Kernel::FT
 linear_least_squares_fitting_3(InputIterator first,
@@ -55,16 +55,16 @@ linear_least_squares_fitting_3(InputIterator first,
                                typename Kernel::Point_3& centroid, 
                                const Tag& tag, // dimension tag, ranges from 0 to 3
 			       const Kernel& kernel,
-			       const Vcm_traits vcm_traits)
+			       const Diagonalize_traits diagonalize_traits)
 {
   typedef typename std::iterator_traits<InputIterator>::value_type Value_type;
   return internal::linear_least_squares_fitting_3(first, beyond, object,
 						  centroid, (Value_type*) NULL, kernel, tag,
-						  vcm_traits);
+						  diagonalize_traits);
 }
 
 // deduces kernel from value type of input iterator
-// use default Vcm_traits
+// use default Diagonalize_traits
 template < typename InputIterator, 
            typename Object,
 	   typename Point,
@@ -81,16 +81,16 @@ linear_least_squares_fitting_3(InputIterator first,
   typedef typename Kernel_traits<Value_type>::Kernel Kernel;
   return CGAL::linear_least_squares_fitting_3(first,beyond,object,centroid,tag,Kernel(),
 #ifdef CGAL_EIGEN3_ENABLED
-					      Eigen_vcm_traits<typename Kernel::FT, 3>()
+					      Eigen_diagonalize_traits<typename Kernel::FT, 3>()
 #else
-					      Internal_vcm_traits<typename Kernel::FT, 3>()
+					      Internal_diagonalize_traits<typename Kernel::FT, 3>()
 #endif
 					      );
 
 }
 
 // deduces kernel and does not write centroid
-// use default Vcm_traits
+// use default Diagonalize_traits
 template < typename InputIterator, 
            typename Object,
            typename Tag>
@@ -106,9 +106,9 @@ linear_least_squares_fitting_3(InputIterator first,
   typename Kernel::Point_3 centroid; // not used by caller
   return CGAL::linear_least_squares_fitting_3(first,beyond,object,centroid,tag,Kernel(),
 #ifdef CGAL_EIGEN3_ENABLED
-					      Eigen_vcm_traits<typename Kernel::FT, 3>()
+					      Eigen_diagonalize_traits<typename Kernel::FT, 3>()
 #else
-					      Internal_vcm_traits<typename Kernel::FT, 3>()
+					      Internal_diagonalize_traits<typename Kernel::FT, 3>()
 #endif
 					      );
 
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h
index b34af34f114..2a13fc63a7a 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_cuboids_3.h
@@ -36,7 +36,7 @@ namespace internal {
 // fits a plane to a 3D cuboid set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -45,7 +45,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Iso_cuboid_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<3>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT FT;
   typedef typename K::Iso_cuboid_3 Iso_cuboid;
@@ -61,7 +61,7 @@ linear_least_squares_fitting_3(InputIterator first,
   assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Iso_cuboid*) NULL,tag);
 
   // compute fitting plane
-  return fitting_plane_3(covariance,c,plane,k,vcm_traits);
+  return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
 
 
 } // end linear_least_squares_fitting_cuboids_3
@@ -69,7 +69,7 @@ linear_least_squares_fitting_3(InputIterator first,
 // fits a plane to a 3D cuboid set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -78,7 +78,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Iso_cuboid_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<2>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT FT;
   typedef typename K::Iso_cuboid_3 Iso_cuboid;
@@ -94,7 +94,7 @@ linear_least_squares_fitting_3(InputIterator first,
   assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Iso_cuboid*) NULL,tag);
 
   // compute fitting plane
-  return fitting_plane_3(covariance,c,plane,k,vcm_traits);
+  return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
 
 
 } // end linear_least_squares_fitting_cuboids_3
@@ -102,7 +102,7 @@ linear_least_squares_fitting_3(InputIterator first,
 // fits a plane to a 3D cuboid set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -111,7 +111,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Iso_cuboid_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<1>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Segment_3 Segment;
   typedef typename K::Iso_cuboid_3 Iso_cuboid;
@@ -141,14 +141,14 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting plane
   return linear_least_squares_fitting_3(segments.begin(),segments.end(),plane,c,(Segment*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_cuboids_3
 
 // fits a plane to a 3D cuboid set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -157,7 +157,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Iso_cuboid_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<0>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Point_3 Point;
   typedef typename K::Iso_cuboid_3 Iso_cuboid;
@@ -183,14 +183,14 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting plane
   return linear_least_squares_fitting_3(points.begin(),points.end(),plane,c,(Point*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_cuboids_3
 
 // fits a line to a 3D cuboid set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -199,7 +199,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Iso_cuboid_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<3>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT FT;
   typedef typename K::Iso_cuboid_3 Iso_cuboid;
@@ -215,14 +215,14 @@ linear_least_squares_fitting_3(InputIterator first,
   assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Iso_cuboid*) NULL,tag);
   
   // compute fitting line
-  return fitting_line_3(covariance,c,line,k,vcm_traits);
+  return fitting_line_3(covariance,c,line,k,diagonalize_traits);
   
 } // end linear_least_squares_fitting_cuboids_3
 
 // fits a line to a 3D cuboid set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -231,7 +231,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Iso_cuboid_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<2>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT FT;
   typedef typename K::Iso_cuboid_3 Iso_cuboid;
@@ -247,7 +247,7 @@ linear_least_squares_fitting_3(InputIterator first,
   assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Iso_cuboid*) NULL,tag);
   
   // compute fitting line
-  return fitting_line_3(covariance,c,line,k,vcm_traits);
+  return fitting_line_3(covariance,c,line,k,diagonalize_traits);
 
 
 } // end linear_least_squares_fitting_cuboids_3
@@ -255,7 +255,7 @@ linear_least_squares_fitting_3(InputIterator first,
 // fits a line to a 3D cuboid set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -264,7 +264,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Iso_cuboid_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<1>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Segment_3 Segment;
   typedef typename K::Iso_cuboid_3 Iso_cuboid;
@@ -294,14 +294,14 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting line
   return linear_least_squares_fitting_3(segments.begin(),segments.end(),line,c,(Segment*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_cuboids_3
 
 // fits a line to a 3D cuboid set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -310,7 +310,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Iso_cuboid_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<0>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Point_3 Point;
   typedef typename K::Iso_cuboid_3 Iso_cuboid;
@@ -336,7 +336,7 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting line
   return linear_least_squares_fitting_3(points.begin(),points.end(),line,c,(Point*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_cuboids_3
 
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_2.h
index 4b43217ce11..19a806d222f 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_2.h
@@ -23,10 +23,10 @@
 #include <CGAL/basic.h>
 #include <CGAL/centroid.h>
 #include <CGAL/eigen_2.h>
-#include <CGAL/Internal_vcm_traits.h>
+#include <CGAL/Internal_diagonalize_traits.h>
 
 #ifdef CGAL_EIGEN3_ENABLED
-#include <CGAL/Eigen_vcm_traits.h>
+#include <CGAL/Eigen_diagonalize_traits.h>
 #endif
 
 #include <iterator>
@@ -43,7 +43,7 @@ namespace internal {
 //              direction by default).
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits>
+	   typename Diagonalize_traits>
 typename K::FT
 linear_least_squares_fitting_2(InputIterator first,
                                InputIterator beyond, 
@@ -52,7 +52,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                const typename K::Point_2*,// used for indirection
                                const K&,                   // kernel
 			       const CGAL::Dimension_tag<0>& tag,
-			       const Vcm_traits&)
+			       const Diagonalize_traits&)
 {
   // types
   typedef typename K::FT       FT;
@@ -91,7 +91,7 @@ linear_least_squares_fitting_2(InputIterator first,
   // eigen vectors are sorted in accordance.
   CGAL::cpp11::array<FT, 2> eigen_values = {{ 0. , 0. }};
   CGAL::cpp11::array<FT, 4> eigen_vectors = {{ 0., 0., 0. }};
-  Vcm_traits::diagonalize_selfadjoint_covariance_matrix
+  Diagonalize_traits::diagonalize_selfadjoint_covariance_matrix
     (covariance, eigen_values, eigen_vectors);
 
   // check unicity and build fitting line accordingly
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_3.h
index ee9603d9cbd..06e63cfbcb7 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_3.h
@@ -35,7 +35,7 @@ namespace internal {
 //  0 is worst (isotropic case, returns a plane with default direction)
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -44,7 +44,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Point_3*, // used for indirection
                                const K& k,                 // kernel
 			       const CGAL::Dimension_tag<0>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT       FT;
   typedef typename K::Point_3  Point;
@@ -60,7 +60,7 @@ linear_least_squares_fitting_3(InputIterator first,
   assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Point*) NULL,tag);
 
   // compute fitting plane
-  return fitting_plane_3(covariance,c,plane,k,vcm_traits);
+  return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
 } // end fit plane to point set
 
 // fits a line to a 3D point set
@@ -69,7 +69,7 @@ linear_least_squares_fitting_3(InputIterator first,
 //  0 is worst (isotropic case, returns a line along x axis)
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -78,7 +78,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Point_3*, // used for indirection
                                const K& k,                // kernel
 			       const CGAL::Dimension_tag<0>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT       FT;
   typedef typename K::Point_3  Point;
@@ -94,7 +94,7 @@ linear_least_squares_fitting_3(InputIterator first,
   assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Point*) NULL,tag);
 
   // compute fitting line
-  return fitting_line_3(covariance,c,line,k,vcm_traits);
+  return fitting_line_3(covariance,c,line,k,diagonalize_traits);
 } // end fit line to point set
 
 } // end namespace internal
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h
index d8d0beece5d..b7201b35d13 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_rectangles_2.h
@@ -38,7 +38,7 @@ namespace internal {
 //  0 is worst (isotropic case, returns a line with horizontal
 //              direction by default)
 
-template < typename InputIterator, typename K, typename Vcm_traits >
+template < typename InputIterator, typename K, typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_2(InputIterator first,
                                InputIterator beyond, 
@@ -47,7 +47,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                const typename K::Iso_rectangle_2*,// used for indirection
                                const K&,                   // kernel
 			       const CGAL::Dimension_tag<2>& tag,
-			       const Vcm_traits&)
+			       const Diagonalize_traits&)
 {
   // types
   typedef typename K::FT       FT;
@@ -128,7 +128,7 @@ linear_least_squares_fitting_2(InputIterator first,
   std::pair<Vector,Vector> eigen_vectors;
   CGAL::cpp11::array<FT, 2> eigen_values1 = {{ 0. , 0. }};
   CGAL::cpp11::array<FT, 4> eigen_vectors1 = {{ 0., 0., 0. }};
-  Vcm_traits::diagonalize_selfadjoint_covariance_matrix
+  Diagonalize_traits::diagonalize_selfadjoint_covariance_matrix
     (covariance, eigen_values1, eigen_vectors1);
 
   eigen_values = std::make_pair(eigen_values1[1],eigen_values1[0]);
@@ -151,7 +151,7 @@ linear_least_squares_fitting_2(InputIterator first,
   } 
 } // end linear_least_squares_fitting_2 for rectangle set with 2D tag
 
-template < typename InputIterator, typename K, typename Vcm_traits >
+template < typename InputIterator, typename K, typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_2(InputIterator first,
                                InputIterator beyond, 
@@ -160,7 +160,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                const typename K::Iso_rectangle_2*,// used for indirection
                                const K&,                   // kernel
 			       const CGAL::Dimension_tag<1>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   // types
   typedef typename K::Iso_rectangle_2 Iso_rectangle;
@@ -182,14 +182,14 @@ linear_least_squares_fitting_2(InputIterator first,
   }    
 
   return linear_least_squares_fitting_2(segments.begin(),segments.end(),line,c,K(),tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_2 for rectangle set with 1D tag
 
 
 template < typename InputIterator,
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_2(InputIterator first,
                                InputIterator beyond, 
@@ -198,7 +198,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                const typename K::Iso_rectangle_2*,// used for indirection
                                const K&,                   // kernel
 			       const CGAL::Dimension_tag<0>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   // types
   typedef typename K::Iso_rectangle_2 Iso_rectangle;
@@ -220,7 +220,7 @@ linear_least_squares_fitting_2(InputIterator first,
   }    
 
   return linear_least_squares_fitting_2(points.begin(),points.end(),line,c,K(),tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_2 for rectangle set with 0D tag
 
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h
index aeb740a4cb6..2fbf05a5e5c 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_2.h
@@ -38,7 +38,7 @@ namespace internal {
 //  0 is worst (isotropic case, returns a line with horizontal
 //              direction by default)
 
-template < typename InputIterator, typename K, typename Vcm_traits >
+template < typename InputIterator, typename K, typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_2(InputIterator first,
                                InputIterator beyond, 
@@ -47,7 +47,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                const typename K::Segment_2*,// used for indirection
                                const K&,                   // kernel
 			       const CGAL::Dimension_tag<1>& tag,
-			       const Vcm_traits&)
+			       const Diagonalize_traits&)
 {
   // types
   typedef typename K::FT       FT;
@@ -116,7 +116,7 @@ linear_least_squares_fitting_2(InputIterator first,
   std::pair<Vector,Vector> eigen_vectors;
   CGAL::cpp11::array<FT, 2> eigen_values1 = {{ 0. , 0. }};
   CGAL::cpp11::array<FT, 4> eigen_vectors1 = {{ 0., 0., 0. }};
-  Vcm_traits::diagonalize_selfadjoint_covariance_matrix
+  Diagonalize_traits::diagonalize_selfadjoint_covariance_matrix
     (covariance, eigen_values1, eigen_vectors1);
 
   eigen_values = std::make_pair(eigen_values1[1],eigen_values1[0]);
@@ -138,7 +138,7 @@ linear_least_squares_fitting_2(InputIterator first,
   } 
 } // end linear_least_squares_fitting_2 for segment set with 1D tag
 
-template < typename InputIterator, typename K, typename Vcm_traits >
+template < typename InputIterator, typename K, typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_2(InputIterator first,
                                InputIterator beyond, 
@@ -147,7 +147,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                const typename K::Segment_2*,// used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<0>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   // types
   typedef typename K::Point_2  Point;
@@ -166,7 +166,7 @@ linear_least_squares_fitting_2(InputIterator first,
     points.push_back(s[1]);
   } 
   return linear_least_squares_fitting_2(points.begin(),points.end(),line,c,k,(Point*)NULL,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_2 for segment set with 1D tag
 
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h
index 1bce41e923b..0eb27f2503f 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_segments_3.h
@@ -35,7 +35,7 @@ namespace internal {
 // fits a plane to a 3D segment set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -44,7 +44,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Segment_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<1>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT          FT;
   typedef typename K::Segment_3  Segment;
@@ -60,14 +60,14 @@ linear_least_squares_fitting_3(InputIterator first,
   assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Segment*) NULL,tag);
 
   // compute fitting plane
-  return fitting_plane_3(covariance,c,plane,k,vcm_traits);
+  return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
 
 } // end linear_least_squares_fitting_segments_3
 
 // fits a plane to a 3D segment set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -76,7 +76,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Segment_3*, // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<0>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Segment_3  Segment;
   typedef typename K::Point_3  Point;
@@ -96,14 +96,14 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting plane
   return linear_least_squares_fitting_3(points.begin(),points.end(),plane,c,(Point*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_segments_3
 
 // fits a line to a 3D segment set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -112,7 +112,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Segment_3*,  // used for indirection
                                const K& k,                    // kernel
 			       const CGAL::Dimension_tag<1>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT          FT;
   typedef typename K::Segment_3  Segment;
@@ -128,14 +128,14 @@ linear_least_squares_fitting_3(InputIterator first,
   assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Segment*) NULL,tag);
 
   // compute fitting line
-  return fitting_line_3(covariance,c,line,k,vcm_traits);
+  return fitting_line_3(covariance,c,line,k,diagonalize_traits);
   
 } // end linear_least_squares_fitting_segments_3
 
 // fits a plane to a 3D segment set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -144,7 +144,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Segment_3*,  // used for indirection
                                const K& k,                    // kernel
 			       const CGAL::Dimension_tag<0>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Segment_3  Segment;
   typedef typename K::Point_3  Point;
@@ -164,7 +164,7 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting plane
   return linear_least_squares_fitting_3(points.begin(),points.end(),line,c,(Point*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_segments_3
 
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_spheres_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_spheres_3.h
index 2a45ee6111b..ad6c35fea34 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_spheres_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_spheres_3.h
@@ -33,7 +33,7 @@ namespace internal {
 // fits a plane to a set of 3D balls (3D)
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -42,7 +42,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Sphere_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<3>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT          FT;
   typedef typename K::Sphere_3    Sphere;
@@ -58,14 +58,14 @@ linear_least_squares_fitting_3(InputIterator first,
   assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Sphere*) NULL,tag);
   
   // compute fitting plane
-  return fitting_plane_3(covariance,c,plane,k,vcm_traits);
+  return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
 
 } // end linear_least_squares_fitting_spheres_3
 
 // fits a plane to a 3D sphere set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -74,7 +74,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Sphere_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<2>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT          FT;
   typedef typename K::Sphere_3    Sphere;
@@ -90,7 +90,7 @@ linear_least_squares_fitting_3(InputIterator first,
   assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Sphere*) NULL,tag);
   
   // compute fitting plane
-  return fitting_plane_3(covariance,c,plane,k,vcm_traits);
+  return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
 
 } // end linear_least_squares_fitting_spheres_3
 
@@ -98,7 +98,7 @@ linear_least_squares_fitting_3(InputIterator first,
 // fits a line to a 3D ball set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -107,7 +107,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Sphere_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<3>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT          FT;
   typedef typename K::Sphere_3  Sphere;
@@ -124,14 +124,14 @@ linear_least_squares_fitting_3(InputIterator first,
 
 
   // compute fitting line
-  return fitting_line_3(covariance,c,line,k,vcm_traits);
+  return fitting_line_3(covariance,c,line,k,diagonalize_traits);
   
 } // end linear_least_squares_fitting_spheres_3
 
 // fits a line to a 3D sphere set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -140,7 +140,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Sphere_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<2>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT          FT;
   typedef typename K::Sphere_3  Sphere;
@@ -156,7 +156,7 @@ linear_least_squares_fitting_3(InputIterator first,
   assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Sphere*) NULL,tag);
 
   // compute fitting line
-  return fitting_line_3(covariance,c,line,k,vcm_traits);
+  return fitting_line_3(covariance,c,line,k,diagonalize_traits);
 
 } // end linear_least_squares_fitting_spheres_3
 
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h
index 2aea4ed6926..bbb6a7b9c26 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_tetrahedra_3.h
@@ -37,7 +37,7 @@ namespace internal {
 // fits a plane to a 3D tetrahedron set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -46,7 +46,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Tetrahedron_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<3>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT          FT;
   typedef typename K::Tetrahedron_3    Tetrahedron;
@@ -62,13 +62,13 @@ linear_least_squares_fitting_3(InputIterator first,
   assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Tetrahedron*) NULL,tag);
   
   // compute fitting plane
-  return fitting_plane_3(covariance,c,plane,k,vcm_traits);
+  return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
 } // end linear_least_squares_fitting_tetrahedrons_3
 
 // fits a plane to a 3D tetrahedron set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -77,7 +77,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Tetrahedron_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<2>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Tetrahedron_3    Tetrahedron;
   typedef typename K::Triangle_3 Triangle;
@@ -99,14 +99,14 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting plane
   return linear_least_squares_fitting_3(triangles.begin(),triangles.end(),plane,c,(Triangle*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_tetrahedrons_3
 
 // fits a plane to a 3D tetrahedron set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -115,7 +115,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Tetrahedron_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<1>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Tetrahedron_3    Tetrahedron;
   typedef typename K::Segment_3 Segment;
@@ -140,14 +140,14 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting plane
   return linear_least_squares_fitting_3(segments.begin(),segments.end(),plane,c,(Segment*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_tetrahedrons_3
 
 // fits a plane to a 3D tetrahedron set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -156,7 +156,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Tetrahedron_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<0>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Tetrahedron_3    Tetrahedron;
   typedef typename K::Point_3 Point;
@@ -178,14 +178,14 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting plane
   return linear_least_squares_fitting_3(points.begin(),points.end(),plane,c,(Point*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_tetrahedrons_3
 
 // fits a line to a 3D tetrahedron set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -194,7 +194,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Tetrahedron_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<3>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT          FT;
   typedef typename K::Tetrahedron_3    Tetrahedron;
@@ -210,14 +210,14 @@ linear_least_squares_fitting_3(InputIterator first,
   assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Tetrahedron*) NULL,tag);
     
   // compute fitting line
-  return fitting_line_3(covariance,c,line,k,vcm_traits);
+  return fitting_line_3(covariance,c,line,k,diagonalize_traits);
   
 } // end linear_least_squares_fitting_tetrahedrons_3
 
 // fits a line to a 3D tetrahedron set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -226,7 +226,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Tetrahedron_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<2>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Tetrahedron_3    Tetrahedron;
   typedef typename K::Triangle_3 Triangle;
@@ -248,14 +248,14 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting line
   return linear_least_squares_fitting_3(triangles.begin(),triangles.end(),line,c,(Triangle*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_tetrahedrons_3
 
 // fits a line to a 3D tetrahedron set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -264,7 +264,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Tetrahedron_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<1>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Tetrahedron_3    Tetrahedron;
   typedef typename K::Segment_3 Segment;
@@ -288,14 +288,14 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting line
   return linear_least_squares_fitting_3(segments.begin(),segments.end(),line,c,(Segment*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_tetrahedrons_3
 
 // fits a line to a 3D tetrahedron set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -304,7 +304,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Tetrahedron_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<0>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Tetrahedron_3    Tetrahedron;
   typedef typename K::Point_3 Point;
@@ -326,7 +326,7 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting line
   return linear_least_squares_fitting_3(points.begin(),points.end(),line,c,(Point*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_tetrahedra_3
 
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_2.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_2.h
index 8cd85dcd167..ee85e40c9c6 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_2.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_2.h
@@ -39,7 +39,7 @@ namespace internal {
 //              direction by default)
 
 template < typename InputIterator,
-           typename Kernel, typename Vcm_traits >
+           typename Kernel, typename Diagonalize_traits >
 typename Kernel::FT
 linear_least_squares_fitting_2(InputIterator first,
                                InputIterator beyond, 
@@ -48,7 +48,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                const typename Kernel::Triangle_2*,// used for indirection
                                const Kernel&,                   // kernel
 			       const CGAL::Dimension_tag<2>& tag,
-			       const Vcm_traits&)
+			       const Diagonalize_traits&)
 {
   // types
   typedef typename Kernel::FT       FT;
@@ -128,7 +128,7 @@ linear_least_squares_fitting_2(InputIterator first,
   std::pair<Vector,Vector> eigen_vectors;
   CGAL::cpp11::array<FT, 2> eigen_values1 = {{ 0. , 0. }};
   CGAL::cpp11::array<FT, 4> eigen_vectors1 = {{ 0., 0., 0. }};
-  Vcm_traits::diagonalize_selfadjoint_covariance_matrix
+  Diagonalize_traits::diagonalize_selfadjoint_covariance_matrix
     (covariance, eigen_values1, eigen_vectors1);
 
   eigen_values = std::make_pair(eigen_values1[1],eigen_values1[0]);
@@ -152,7 +152,7 @@ linear_least_squares_fitting_2(InputIterator first,
 
 template < typename InputIterator,
            typename Kernel,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename Kernel::FT
 linear_least_squares_fitting_2(InputIterator first,
                                InputIterator beyond, 
@@ -161,7 +161,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                const typename Kernel::Triangle_2*,// used for indirection
                                const Kernel&,                   // kernel
 			       const CGAL::Dimension_tag<1>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   // types
   typedef typename Kernel::Triangle_2 Triangle;
@@ -182,13 +182,13 @@ linear_least_squares_fitting_2(InputIterator first,
   }    
   
   return linear_least_squares_fitting_2(segments.begin(),segments.end(),line,c,tag,Kernel(),
-					vcm_traits);
+					diagonalize_traits);
   
 } // end linear_least_squares_fitting_2 for triangle set with 1D tag
 
 template < typename InputIterator,
            typename Kernel,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename Kernel::FT
 linear_least_squares_fitting_2(InputIterator first,
                                InputIterator beyond, 
@@ -197,7 +197,7 @@ linear_least_squares_fitting_2(InputIterator first,
                                const typename Kernel::Triangle_2*,// used for indirection
                                const Kernel&,                   // kernel
 			       const CGAL::Dimension_tag<0>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   // types
 
@@ -219,7 +219,7 @@ linear_least_squares_fitting_2(InputIterator first,
   }    
   
   return linear_least_squares_fitting_2(points.begin(),points.end(),line,c,tag,Kernel(),
-					vcm_traits);
+					diagonalize_traits);
   
 } // end linear_least_squares_fitting_2 for triangle set with 0D tag
 
diff --git a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h
index aabc8fe0b1b..dc305ea73a6 100644
--- a/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h
+++ b/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_triangles_3.h
@@ -34,7 +34,7 @@ namespace internal {
 // fits a plane to a 3D triangle set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -43,7 +43,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Triangle_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<2>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT          FT;
   typedef typename K::Triangle_3  Triangle;
@@ -59,14 +59,14 @@ linear_least_squares_fitting_3(InputIterator first,
   assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Triangle*) NULL,tag);
   
   // compute fitting plane
-  return fitting_plane_3(covariance,c,plane,k,vcm_traits);
+  return fitting_plane_3(covariance,c,plane,k,diagonalize_traits);
 
 } // end linear_least_squares_fitting_triangles_3
 
 // fits a plane to a 3D triangle set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -75,7 +75,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Triangle_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<1>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Triangle_3  Triangle;
   typedef typename K::Segment_3  Segment;
@@ -96,14 +96,14 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting plane
   return linear_least_squares_fitting_3(segments.begin(),segments.end(),plane,c,(Segment*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_triangles_3
 
 // fits a plane to a 3D triangle set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -112,7 +112,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Triangle_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<0>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Triangle_3  Triangle;
   typedef typename K::Point_3  Point;
@@ -132,14 +132,14 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting plane
   return linear_least_squares_fitting_3(points.begin(),points.end(),plane,c,(Point*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_triangles_3
 
 // fits a line to a 3D triangle set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -148,7 +148,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Triangle_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<2>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::FT          FT;
   typedef typename K::Triangle_3  Triangle;
@@ -164,14 +164,14 @@ linear_least_squares_fitting_3(InputIterator first,
   assemble_covariance_matrix_3(first,beyond,covariance,c,k,(Triangle*) NULL,tag);
 
   // compute fitting line
-  return fitting_line_3(covariance,c,line,k,vcm_traits);
+  return fitting_line_3(covariance,c,line,k,diagonalize_traits);
   
 } // end linear_least_squares_fitting_triangles_3
 
 // fits a line to a 3D triangle set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -180,7 +180,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Triangle_3*,  // used for indirection
                                const K& k,                   // kernel
 			       const CGAL::Dimension_tag<1>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Triangle_3  Triangle;
   typedef typename K::Segment_3  Segment;
@@ -201,14 +201,14 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting line
   return linear_least_squares_fitting_3(segments.begin(),segments.end(),line,c,(Segment*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_triangles_3
 
 // fits a line to a 3D triangle set
 template < typename InputIterator, 
            typename K,
-	   typename Vcm_traits >
+	   typename Diagonalize_traits >
 typename K::FT
 linear_least_squares_fitting_3(InputIterator first,
                                InputIterator beyond, 
@@ -217,7 +217,7 @@ linear_least_squares_fitting_3(InputIterator first,
                                const typename K::Triangle_3*,  // used for indirection
                                const K& k,                   // kernel
                                const CGAL::Dimension_tag<0>& tag,
-			       const Vcm_traits& vcm_traits)
+			       const Diagonalize_traits& diagonalize_traits)
 {
   typedef typename K::Triangle_3  Triangle;
   typedef typename K::Point_3  Point;
@@ -237,7 +237,7 @@ linear_least_squares_fitting_3(InputIterator first,
 
   // compute fitting line
   return linear_least_squares_fitting_3(points.begin(),points.end(),line,c,(Point*)NULL,k,tag,
-					vcm_traits);
+					diagonalize_traits);
 
 } // end linear_least_squares_fitting_triangles_3
 
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_2.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_2.cpp
index 86bc9a4327d..5ad47866509 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_2.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_2.cpp
@@ -3,10 +3,10 @@
 #include <CGAL/algorithm.h>
 #include <CGAL/linear_least_squares_fitting_2.h>
 #include <CGAL/point_generators_2.h>
-#include <CGAL/Internal_vcm_traits.h>
+#include <CGAL/Internal_diagonalize_traits.h>
 
 #ifdef CGAL_EIGEN3_ENABLED
-#include <CGAL/Eigen_vcm_traits.h>
+#include <CGAL/Eigen_diagonalize_traits.h>
 #endif
 
 #include <vector>
@@ -38,9 +38,9 @@ void test_2D()
   quality = linear_least_squares_fitting_2(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>());
   quality = linear_least_squares_fitting_2(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>(),k,
 #ifdef CGAL_EIGEN3_ENABLED
-					   CGAL::Eigen_vcm_traits<typename Kernel::FT, 2>()
+					   CGAL::Eigen_diagonalize_traits<typename Kernel::FT, 2>()
 #else
-					   CGAL::Internal_vcm_traits<typename Kernel::FT, 2>()
+					   CGAL::Internal_diagonalize_traits<typename Kernel::FT, 2>()
 #endif
 					   );
   
@@ -85,9 +85,9 @@ void test_2D_point_set(const unsigned int nb_points)
   quality = linear_least_squares_fitting_2(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>());
   quality = linear_least_squares_fitting_2(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>(),k,
 #ifdef CGAL_EIGEN3_ENABLED
-					   CGAL::Eigen_vcm_traits<typename Kernel::FT, 2>()
+					   CGAL::Eigen_diagonalize_traits<typename Kernel::FT, 2>()
 #else
-					   CGAL::Internal_vcm_traits<typename Kernel::FT, 2>()
+					   CGAL::Internal_diagonalize_traits<typename Kernel::FT, 2>()
 #endif
 					   );
   std::cout << "done (quality: " << quality << ")" << std::endl;
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_3.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_3.cpp
index f39794f2756..6a1399e6204 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_3.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_points_3.cpp
@@ -3,9 +3,9 @@
 
 #include <CGAL/Cartesian.h>
 #include <CGAL/linear_least_squares_fitting_3.h>
-#include <CGAL/Internal_vcm_traits.h>
+#include <CGAL/Internal_diagonalize_traits.h>
 #ifdef CGAL_EIGEN3_ENABLED
-#include <CGAL/Eigen_vcm_traits.h>
+#include <CGAL/Eigen_diagonalize_traits.h>
 #endif
 
 #include <cassert>
@@ -50,9 +50,9 @@ void fit_point_set(std::list<Point>& points,
   quality = linear_least_squares_fitting_3(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>());
   quality = linear_least_squares_fitting_3(points.begin(),points.end(),line,centroid,CGAL::Dimension_tag<0>(),kernel,
 #ifdef CGAL_EIGEN3_ENABLED
-					   CGAL::Eigen_vcm_traits<typename Kernel::FT, 3>()
+					   CGAL::Eigen_diagonalize_traits<typename Kernel::FT, 3>()
 #else
-					   CGAL::Internal_vcm_traits<typename Kernel::FT, 3>()
+					   CGAL::Internal_diagonalize_traits<typename Kernel::FT, 3>()
 #endif
 					   );
 
@@ -63,9 +63,9 @@ void fit_point_set(std::list<Point>& points,
   quality = linear_least_squares_fitting_3(points.begin(),points.end(),plane,centroid,CGAL::Dimension_tag<0>());
   quality = linear_least_squares_fitting_3(points.begin(),points.end(),plane,centroid,CGAL::Dimension_tag<0>(),kernel,
 #ifdef CGAL_EIGEN3_ENABLED
-					   CGAL::Eigen_vcm_traits<typename Kernel::FT, 3>()
+					   CGAL::Eigen_diagonalize_traits<typename Kernel::FT, 3>()
 #else
-					   CGAL::Internal_vcm_traits<typename Kernel::FT, 3>()
+					   CGAL::Internal_diagonalize_traits<typename Kernel::FT, 3>()
 #endif
 					   );
   std::cout << "done (quality: " << quality << ")" << std::endl;
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_segments_3.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_segments_3.cpp
index 3d774c7e782..54df04e3094 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_segments_3.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_segments_3.cpp
@@ -5,9 +5,9 @@
 #include <CGAL/algorithm.h>
 #include <CGAL/linear_least_squares_fitting_3.h>
 #include <CGAL/point_generators_3.h>
-#include <CGAL/Internal_vcm_traits.h>
+#include <CGAL/Internal_diagonalize_traits.h>
 #ifdef CGAL_EIGEN3_ENABLED
-#include <CGAL/Eigen_vcm_traits.h>
+#include <CGAL/Eigen_diagonalize_traits.h>
 #endif
 
 #include <vector>
@@ -40,9 +40,9 @@ FT fit_set(std::list<Segment>& segments,
   quality = linear_least_squares_fitting_3(segments.begin(),segments.end(),line,centroid,CGAL::Dimension_tag<1>());
   quality = linear_least_squares_fitting_3(segments.begin(),segments.end(),line,centroid,CGAL::Dimension_tag<1>(),kernel,
 #ifdef CGAL_EIGEN3_ENABLED
-					   CGAL::Eigen_vcm_traits<typename Kernel::FT, 3>()
+					   CGAL::Eigen_diagonalize_traits<typename Kernel::FT, 3>()
 #else
-					   CGAL::Internal_vcm_traits<typename Kernel::FT, 3>()
+					   CGAL::Internal_diagonalize_traits<typename Kernel::FT, 3>()
 #endif
 					   );
 
@@ -51,9 +51,9 @@ FT fit_set(std::list<Segment>& segments,
   quality = linear_least_squares_fitting_3(segments.begin(),segments.end(),plane,centroid,CGAL::Dimension_tag<1>());
   quality = linear_least_squares_fitting_3(segments.begin(),segments.end(),plane,centroid,CGAL::Dimension_tag<1>(),kernel,
 #ifdef CGAL_EIGEN3_ENABLED
-					   CGAL::Eigen_vcm_traits<typename Kernel::FT, 3>()
+					   CGAL::Eigen_diagonalize_traits<typename Kernel::FT, 3>()
 #else
-					   CGAL::Internal_vcm_traits<typename Kernel::FT, 3>()
+					   CGAL::Internal_diagonalize_traits<typename Kernel::FT, 3>()
 #endif
 					   );
 
diff --git a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_spheres_3.cpp b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_spheres_3.cpp
index 2c6eb36230f..6cbdacb4740 100644
--- a/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_spheres_3.cpp
+++ b/Principal_component_analysis/test/Principal_component_analysis/test_linear_least_squares_fitting_spheres_3.cpp
@@ -35,9 +35,9 @@ int main(void)
   Point centroid;
 
 #ifdef CGAL_EIGEN3_ENABLED
-  CGAL::Eigen_vcm_traits<typename Kernel::FT, 3> vcm_traits;
+  CGAL::Eigen_diagonalize_traits<typename Kernel::FT, 3> diagonalize_traits;
 #else
-  CGAL::Internal_vcm_traits<typename Kernel::FT, 3> vcm_traits;
+  CGAL::Internal_diagonalize_traits<typename Kernel::FT, 3> diagonalize_traits;
 #endif
 
   linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,CGAL::Dimension_tag<3>());
@@ -45,17 +45,17 @@ int main(void)
   linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,centroid,CGAL::Dimension_tag<3>());
   linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,centroid,CGAL::Dimension_tag<2>());
   linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,centroid,CGAL::Dimension_tag<3>(),kernel,
-				 vcm_traits);
+				 diagonalize_traits);
   linear_least_squares_fitting_3(spheres.begin(),spheres.end(),line,centroid,CGAL::Dimension_tag<2>(),kernel,
-				 vcm_traits);
+				 diagonalize_traits);
   linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,CGAL::Dimension_tag<3>());
   linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,CGAL::Dimension_tag<2>());
   linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,centroid,CGAL::Dimension_tag<3>());
   linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,centroid,CGAL::Dimension_tag<2>());
   linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,centroid,CGAL::Dimension_tag<3>(),kernel,
-				 vcm_traits);
+				 diagonalize_traits);
   linear_least_squares_fitting_3(spheres.begin(),spheres.end(),plane,centroid,CGAL::Dimension_tag<2>(),kernel,
-				 vcm_traits);
+				 diagonalize_traits);
 
   return 0;
 }
diff --git a/Solver_interface/doc/Solver_interface/CGAL/Eigen_vcm_traits.h b/Solver_interface/doc/Solver_interface/CGAL/Eigen_diagonalize_traits.h
similarity index 78%
rename from Solver_interface/doc/Solver_interface/CGAL/Eigen_vcm_traits.h
rename to Solver_interface/doc/Solver_interface/CGAL/Eigen_diagonalize_traits.h
index 9831893a6ec..aee2d3363b6 100644
--- a/Solver_interface/doc/Solver_interface/CGAL/Eigen_vcm_traits.h
+++ b/Solver_interface/doc/Solver_interface/CGAL/Eigen_diagonalize_traits.h
@@ -3,10 +3,14 @@ namespace CGAL {
 /*!
 \ingroup PkgSolver
 
-The class `Eigen_vcm_traits` provides an interface to the diagonalization of Variance-Covariance Matrices of \ref thirdpartyEigen "Eigen".
-The version 3.1 (or greater) of \ref thirdpartyEigen "Eigen" must be available on the system. 
+The class `Eigen_diagonalize_traits` provides an interface to the
+diagonalization of covariance matrices of \ref thirdpartyEigen
+"Eigen".
 
-\cgalModels `VCMTraits`
+The version 3.1 (or greater) of \ref thirdpartyEigen "Eigen" must be
+available on the system.
+
+\cgalModels `DiagonalizeTraits`
 
 
 `FT`: floating type
@@ -24,7 +28,7 @@ Example
 
   
 template <typename FT, unsigned int dim = 3>
-class Eigen_vcm_traits{
+class Eigen_diagonalize_traits{
 
 public:
   static bool
diff --git a/Solver_interface/doc/Solver_interface/CGAL/Internal_vcm_traits.h b/Solver_interface/doc/Solver_interface/CGAL/Internal_diagonalize_traits.h
similarity index 78%
rename from Solver_interface/doc/Solver_interface/CGAL/Internal_vcm_traits.h
rename to Solver_interface/doc/Solver_interface/CGAL/Internal_diagonalize_traits.h
index 0af6d0bbcae..44699475782 100644
--- a/Solver_interface/doc/Solver_interface/CGAL/Internal_vcm_traits.h
+++ b/Solver_interface/doc/Solver_interface/CGAL/Internal_diagonalize_traits.h
@@ -3,9 +3,11 @@ namespace CGAL {
 /*!
 \ingroup PkgSolver
 
-The class `Internal_vcm_traits` provides an internal implementation for the diagonalization of Variance-Covariance Matrices.
+The class `Internal_diagonalize_traits` provides an internal
+implementation for the diagonalization of Variance-Covariance
+Matrices.
 
-\cgalModels `VCMTraits`
+\cgalModels `DiagonalizeTraits`
 
 
 `FT`: floating type
@@ -20,7 +22,7 @@ Example
 
   
 template <typename FT, unsigned int dim = 3>
-class Internal_vcm_traits{
+class Internal_diagonalize_traits{
 
 public:
   static bool
diff --git a/Solver_interface/doc/Solver_interface/Concepts/VCMTraits.h b/Solver_interface/doc/Solver_interface/Concepts/DiagonalizeTraits.h
similarity index 84%
rename from Solver_interface/doc/Solver_interface/Concepts/VCMTraits.h
rename to Solver_interface/doc/Solver_interface/Concepts/DiagonalizeTraits.h
index 4befedd5e5b..00341ec9266 100644
--- a/Solver_interface/doc/Solver_interface/Concepts/VCMTraits.h
+++ b/Solver_interface/doc/Solver_interface/Concepts/DiagonalizeTraits.h
@@ -3,8 +3,9 @@
 \cgalConcept
 
 Concept providing functions to extract eigenvectors and eigenvalue
-from covariance matrices represented by an array `a`. For example, a
-matrix of dimension 3 is defined as follows:
+from covariance matrices represented by an array `a`, using symmetric
+diagonalization. For example, a matrix of dimension 3 is defined as
+follows:
 <center>
 \f$ \begin{bmatrix}
   a[0] & a[1] & a[2] \\
@@ -12,11 +13,11 @@ matrix of dimension 3 is defined as follows:
   a[2] & a[4] & a[5] \\
  \end{bmatrix}\f$
 </center>
-\cgalHasModel `CGAL::Eigen_vcm_traits`
-\cgalHasModel `CGAL::Internal_vcm_traits`
+\cgalHasModel `CGAL::Eigen_diagonalize_traits`
+\cgalHasModel `CGAL::Internal_diagonalize_traits`
 */
 template <typename FT, unsigned int dim = 3>
-class VCMTraits
+class DiagonalizeTraits
 {
 public:
   /// fill `eigenvalues` with the eigenvalues of the covariance matrix represented by `cov`.
diff --git a/Solver_interface/doc/Solver_interface/PackageDescription.txt b/Solver_interface/doc/Solver_interface/PackageDescription.txt
index 1713c6412e2..c076230edfb 100644
--- a/Solver_interface/doc/Solver_interface/PackageDescription.txt
+++ b/Solver_interface/doc/Solver_interface/PackageDescription.txt
@@ -28,17 +28,19 @@
 - `SparseLinearAlgebraTraits_d`
 - `SparseLinearAlgebraTraitsWithFactor_d`
 - `SvdTraits`
-- `VCMTraits`
+- `DiagonalizeTraits`
 
 ## Classes ##
 
 - `CGAL::Eigen_solver_traits`
 - `CGAL::Eigen_svd`
-- `CGAL::Eigen_vcm_traits`
+- `CGAL::Eigen_diagonalize_traits`
 - `CGAL::Eigen_matrix`
 - `CGAL::Eigen_vector`
 - `CGAL::Eigen_sparse_matrix`
 - `CGAL::Eigen_sparse_symmetric_matrix`
+- `CGAL::Internal_diagonalize_traits`
+- `CGAL::Lapack_svd`
 
 */
 
diff --git a/Solver_interface/doc/Solver_interface/Solver_interface.txt b/Solver_interface/doc/Solver_interface/Solver_interface.txt
index b2102ef6689..d2cc68e8cbb 100644
--- a/Solver_interface/doc/Solver_interface/Solver_interface.txt
+++ b/Solver_interface/doc/Solver_interface/Solver_interface.txt
@@ -16,20 +16,20 @@ equivalent models for other solvers, for example those found in the
 <a href="https://software.intel.com/en-us/intel-mkl">Intel Math Kernel Library (MKL)</a>.
 
 
-\section SectionSolverVCM Matrix Diagonalization
+\section SectionSolverDiagonalize Matrix Diagonalization
 
-The concept `VCMTraits<T,dim>` defines an interface for the
+The concept `DiagonalizeTraits<T,dim>` defines an interface for the
 diagonalization and computation of eigenvectors and eigenvalues of a
 symmetric matrix. `T` is the number type and `dim` is the dimension of
 the matrices and vector (set to 3 by default). We provide two models
 for this concept:
 
-- `Eigen_vcm_traits<T,dim>` uses the \ref thirdpartyEigen library.
-- `Internal_vcm_traits<T,dim>` is an internal implementation that does not
+- `Eigen_diagonalize_traits<T,dim>` uses the \ref thirdpartyEigen library.
+- `Internal_diagonalize_traits<T,dim>` is an internal implementation that does not
 depend on another library.
 
 Although both models achieve the same computation,
-`Eigen_vcm_traits<T,dim>` is faster and should thus be used if the
+`Eigen_diagonalize_traits<T,dim>` is faster and should thus be used if the
 \ref thirdpartyEigen library is available. The eigenvalues are stored
 in ascending order and eigenvectors are stored in accordance.
 
diff --git a/Solver_interface/examples/Solver_interface/diagonalize_matrix.cpp b/Solver_interface/examples/Solver_interface/diagonalize_matrix.cpp
index b092ff87fcf..ef96a3cd5c2 100644
--- a/Solver_interface/examples/Solver_interface/diagonalize_matrix.cpp
+++ b/Solver_interface/examples/Solver_interface/diagonalize_matrix.cpp
@@ -1,9 +1,9 @@
 #include <iostream>
 
 #ifdef CGAL_EIGEN3_ENABLED
-#include <CGAL/Eigen_vcm_traits.h>
+#include <CGAL/Eigen_diagonalize_traits.h>
 #else
-#include <CGAL/Internal_vcm_traits.h>
+#include <CGAL/Internal_diagonalize_traits.h>
 #endif
 
 
@@ -12,9 +12,9 @@ typedef CGAL::cpp11::array<FT, 6> Eigen_matrix;
 typedef CGAL::cpp11::array<FT, 3> Eigen_vector;
 typedef CGAL::cpp11::array<FT, 9> Eigen_three_vectors;
 #ifdef CGAL_EIGEN3_ENABLED
-typedef CGAL::Eigen_vcm_traits<FT, 3> Vcm_traits;
+typedef CGAL::Eigen_diagonalize_traits<FT, 3> Diagonalize_traits;
 #else
-typedef CGAL::Internal_vcm_traits<FT, 3> Vcm_traits;
+typedef CGAL::Internal_diagonalize_traits<FT, 3> Diagonalize_traits;
 #endif
 
 int main(void)
@@ -27,9 +27,9 @@ int main(void)
   Eigen_vector eigenvalues;
   Eigen_three_vectors eigenvectors;
 
-  if (!(Vcm_traits::diagonalize_selfadjoint_covariance_matrix (covariance,
-							       eigenvalues,
-							       eigenvectors)))
+  if (!(Diagonalize_traits::diagonalize_selfadjoint_covariance_matrix (covariance,
+								       eigenvalues,
+								       eigenvectors)))
     {
       std::cerr << "Error: cannot diagonalize matrix" << std::endl;
       return -1;
diff --git a/Solver_interface/include/CGAL/Eigen_vcm_traits.h b/Solver_interface/include/CGAL/Eigen_diagonalize_traits.h
similarity index 93%
rename from Solver_interface/include/CGAL/Eigen_vcm_traits.h
rename to Solver_interface/include/CGAL/Eigen_diagonalize_traits.h
index edc7de0d763..9be27f3c27a 100644
--- a/Solver_interface/include/CGAL/Eigen_vcm_traits.h
+++ b/Solver_interface/include/CGAL/Eigen_diagonalize_traits.h
@@ -18,8 +18,8 @@
 // Author(s) : Jocelyn Meyron and Quentin Mérigot
 //
 
-#ifndef CGAL_EIGEN_VCM_TRAITS_H
-#define CGAL_EIGEN_VCM_TRAITS_H
+#ifndef CGAL_EIGEN_DIAGONALIZE_TRAITS_H
+#define CGAL_EIGEN_DIAGONALIZE_TRAITS_H
 
 #include <Eigen/Dense>
 #include <Eigen/Eigenvalues>
@@ -28,11 +28,11 @@
 
 namespace CGAL {
 
-/// A model of the concept `VCMTraits` using \ref thirdpartyEigen.
-/// \cgalModels `VCMTraits`
+/// A model of the concept `DiagonalizeTraits` using \ref thirdpartyEigen.
+/// \cgalModels `DiagonalizeTraits`
 
 template <typename FT, unsigned int dim = 3>
-class Eigen_vcm_traits{
+class Eigen_diagonalize_traits{
 
   typedef Eigen::Matrix<FT, dim, dim> Matrix;
   typedef Eigen::Matrix<FT, dim, 1> Vector;
@@ -146,4 +146,4 @@ public:
 
 } // namespace CGAL
 
-#endif // CGAL_EIGEN_VCM_TRAITS_H
+#endif // CGAL_EIGEN_DIAGONALIZE_TRAITS_H
diff --git a/Solver_interface/include/CGAL/Internal_vcm_traits.h b/Solver_interface/include/CGAL/Internal_diagonalize_traits.h
similarity index 95%
rename from Solver_interface/include/CGAL/Internal_vcm_traits.h
rename to Solver_interface/include/CGAL/Internal_diagonalize_traits.h
index 57f3bc10735..8d6bbee1993 100644
--- a/Solver_interface/include/CGAL/Internal_vcm_traits.h
+++ b/Solver_interface/include/CGAL/Internal_diagonalize_traits.h
@@ -1,15 +1,15 @@
-#ifndef CGAL_INTERNAL_VCM_TRAITS_H
-#define CGAL_INTERNAL_VCM_TRAITS_H
+#ifndef CGAL_INTERNAL_DIAGONALIZE_TRAITS_H
+#define CGAL_INTERNAL_DIAGONALIZE_TRAITS_H
 
 #include <CGAL/array.h>
 
 namespace CGAL {
 
-  /// A model of the concept `VCMTraits` 
-  /// \cgalModels `VCMTraits`
+  /// A model of the concept `DiagonalizeTraits` 
+  /// \cgalModels `DiagonalizeTraits`
 
 template <typename FT, unsigned int dim = 3>
-class Internal_vcm_traits{
+class Internal_diagonalize_traits{
 
  public:
     static bool
@@ -244,4 +244,4 @@ class Internal_vcm_traits{
 
 } // namespace CGAL
 
-#endif // CGAL_INTERNAL_VCM_TRAITS_H
+#endif // CGAL_INTERNAL_DIAGONALIZE_TRAITS_H