diff --git a/dune/matrix-vector/algorithm.hh b/dune/matrix-vector/algorithm.hh
index 3fb24530a73a2d4de4947d003c180ae1eccc6ca1..81d55f7ee8724d1051b80fd9826c91337a9042a7 100644
--- a/dune/matrix-vector/algorithm.hh
+++ b/dune/matrix-vector/algorithm.hh
@@ -4,13 +4,13 @@
 #define DUNE_MATRIX_VECTOR_ALGORITHM_HH
 
 #include <dune/common/hybridutilities.hh>
-#include <dune/matrix-vector/traitutilities.hh>
+#include <dune/matrix-vector/traits/utilities.hh>
 
 namespace Dune {
 namespace MatrixVector {
 
 //! \brief Hybrid for loop over sparse range (static/tuple-like candidate)
-template <class Range, class F, std::enable_if_t<isTupleOrDerived<Range>(), int> = 0>
+template <class Range, class F, EnableTupleOrDerived<Range, int> = 0>
 void sparseRangeFor(Range&& range, F&& f) {
   using namespace Dune::Hybrid;
   forEach(integralRange(size(range)), [&](auto&& i) {
@@ -19,7 +19,7 @@ void sparseRangeFor(Range&& range, F&& f) {
 }
 
 //! \brief Hybrid for loop over sparse range (dynamic/sparse candidate)
-template<class Range, class F, std::enable_if_t<not isTupleOrDerived<Range>(), int> = 0>
+template<class Range, class F, DisableTupleOrDerived<Range, int> = 0>
 void sparseRangeFor(Range&& range, F&& f)
 {
   auto it = range.begin();
@@ -29,12 +29,12 @@ void sparseRangeFor(Range&& range, F&& f)
 }
 
 //! \brief Hybrid access to first sparse range element (static/tuple-like candiate)
-template <class Range, class F, std::enable_if_t<isTupleOrDerived<Range>(), int> = 0>
+template <class Range, class F, EnableTupleOrDerived<Range, int> = 0>
 void sparseRangeFirst(Range&& range, F&& f) {
   f(range[Indices::_0]);
 }
 //! \brief Hybrid access to first sparse range element (dynamic/sparse candiate)
-template<class Range, class F, std::enable_if_t<not isTupleOrDerived<Range>(), int> = 0>
+template <class Range, class F, DisableTupleOrDerived<Range, int> = 0>
 void sparseRangeFirst(Range&& range, F&& f)
 {
   f(*range.begin());
diff --git a/dune/matrix-vector/axpy.hh b/dune/matrix-vector/axpy.hh
index fe6740fa48755669a4eea8be4026b29a12784a52..4672c202c1c00da05c6c00acf4c170065b58d3ab 100644
--- a/dune/matrix-vector/axpy.hh
+++ b/dune/matrix-vector/axpy.hh
@@ -8,9 +8,8 @@
 #include <dune/istl/bcrsmatrix.hh>
 #include <dune/istl/scaledidmatrix.hh>
 
-#include "algorithm.hh"
-#include "matrixtraits.hh"
-#include "scalartraits.hh"
+#include <dune/matrix-vector/algorithm.hh>
+#include <dune/matrix-vector/traits/utilities.hh>
 
 namespace Dune {
 namespace MatrixVector {
@@ -38,8 +37,8 @@ namespace MatrixVector {
    */
   template <class A, class B, class C>
   void addProduct(A& a, const B& b, const C& c) {
-    ProductHelper<A, B, C, ScalarTraits<A>::isScalar, ScalarTraits<B>::isScalar,
-                  ScalarTraits<C>::isScalar>::addProduct(a, b, c);
+    ProductHelper<A, B, C, isScalar<A>(), isScalar<B>(),
+                  isScalar<C>()>::addProduct(a, b, c);
   }
 
   /** \brief Subtract a product from some matrix or vector
@@ -55,9 +54,8 @@ namespace MatrixVector {
    */
   template <class A, class B, class C>
   void subtractProduct(A& a, const B& b, const C& c) {
-    ScaledProductHelper<A, int, B, C, ScalarTraits<A>::isScalar,
-                        ScalarTraits<B>::isScalar,
-                        ScalarTraits<C>::isScalar>::addProduct(a, -1, b, c);
+    ScaledProductHelper<A, int, B, C, isScalar<A>(), isScalar<B>(),
+                        isScalar<C>()>::addProduct(a, -1, b, c);
   }
 
   /** \brief Add a scaled product to some matrix or vector
@@ -72,11 +70,10 @@ namespace MatrixVector {
    * 1-dim vector or a 1 by 1 matrix.
    */
   template <class A, class B, class C, class D>
-  typename std::enable_if_t<ScalarTraits<B>::isScalar, void> addProduct(
+  EnableScalar<B> addProduct(
       A& a, const B& b, const C& c, const D& d) {
-    ScaledProductHelper<A, B, C, D, ScalarTraits<A>::isScalar,
-                        ScalarTraits<C>::isScalar,
-                        ScalarTraits<D>::isScalar>::addProduct(a, b, c, d);
+    ScaledProductHelper<A, B, C, D, isScalar<A>(), isScalar<C>(),
+                        isScalar<D>()>::addProduct(a, b, c, d);
   }
 
   /** \brief Subtract a scaled product from some matrix or vector
@@ -91,11 +88,10 @@ namespace MatrixVector {
    * 1-dim vector or a 1 by 1 matrix.
    */
   template <class A, class B, class C, class D>
-  typename std::enable_if_t<ScalarTraits<B>::isScalar, void>
+  EnableScalar<B>
   subtractProduct(A& a, const B& b, const C& c, const D& d) {
-    ScaledProductHelper<A, B, C, D, ScalarTraits<A>::isScalar,
-                        ScalarTraits<C>::isScalar,
-                        ScalarTraits<D>::isScalar>::addProduct(a, -b, c, d);
+    ScaledProductHelper<A, B, C, D, isScalar<A>(), isScalar<C>(),
+                        isScalar<D>()>::addProduct(a, -b, c, d);
   }
 
   /** \brief Internal helper class for product operations
@@ -104,16 +100,12 @@ namespace MatrixVector {
   template <class A, class B, class C, bool AisScalar, bool BisScalar,
             bool CisScalar>
   struct ProductHelper {
-    template <
-        class ADummy = A,
-        std::enable_if_t<!MatrixTraits<ADummy>::isMatrix, int> SFINAE_Dummy = 0>
+    template <class ADummy = A, DisableMatrix<ADummy, int> = 0>
     static void addProduct(A& a, const B& b, const C& c) {
       b.umv(c, a);
     }
 
-    template <
-        class ADummy = A,
-        std::enable_if_t<MatrixTraits<ADummy>::isMatrix, int> SFINAE_Dummy = 0>
+    template <class ADummy = A, EnableMatrix<ADummy, int> = 0>
     static void addProduct(A& a, const B& b, const C& c) {
       sparseRangeFor(b, [&](auto&& bi, auto&& i) {
         sparseRangeFor(bi, [&](auto&& bik, auto&& k) {
@@ -130,16 +122,12 @@ namespace MatrixVector {
   template <class A, class Scalar, class B, class C, bool AisScalar,
             bool BisScalar, bool CisScalar>
   struct ScaledProductHelper {
-    template <
-        class ADummy = A,
-        std::enable_if_t<!MatrixTraits<ADummy>::isMatrix, int> SFINAE_Dummy = 0>
+    template <class ADummy = A, DisableMatrix<ADummy, int> = 0>
     static void addProduct(A& a, const Scalar& scalar, const B& b, const C& c) {
       b.usmv(scalar, c, a);
     }
 
-    template <
-        class ADummy = A,
-        std::enable_if_t<MatrixTraits<ADummy>::isMatrix, int> SFINAE_Dummy = 0>
+    template <class ADummy = A, EnableMatrix<ADummy, int> = 0>
     static void addProduct(A& a, const Scalar& scalar, const B& b, const C& c) {
       sparseRangeFor(b, [&](auto&& bi, auto&& i) {
         sparseRangeFor(bi, [&](auto&& bik, auto&& k) {
@@ -317,16 +305,12 @@ namespace MatrixVector {
   struct ProductHelper<A, ScalarB, C, AisScalar, true, CisScalar> {
     typedef ScalarB B;
 
-    template <
-        class ADummy = A,
-        std::enable_if_t<!MatrixTraits<ADummy>::isMatrix, int> SFINAE_Dummy = 0>
+    template <class ADummy = A, DisableMatrix<ADummy, int> = 0>
     static void addProduct(A& a, const B& b, const C& c) {
       a.axpy(b, c);
     }
 
-    template <
-        class ADummy = A,
-        std::enable_if_t<MatrixTraits<ADummy>::isMatrix, int> SFINAE_Dummy = 0>
+    template <class ADummy = A, EnableMatrix<ADummy, int> = 0>
     static void addProduct(A& a, const B& b, const C& c) {
       sparseRangeFor(c, [&](auto&& ci, auto && i) {
         sparseRangeFor(ci, [&](auto&& cij, auto && j) {
@@ -342,16 +326,12 @@ namespace MatrixVector {
                              CisScalar> {
     typedef ScalarB B;
 
-    template <
-        class ADummy = A,
-        std::enable_if_t<!MatrixTraits<ADummy>::isMatrix, int> SFINAE_Dummy = 0>
+    template <class ADummy = A, DisableMatrix<ADummy, int> = 0>
     static void addProduct(A& a, const Scalar& scalar, const B& b, const C& c) {
       a.axpy(scalar * b, c);
     }
 
-    template <
-        class ADummy = A,
-        std::enable_if_t<MatrixTraits<ADummy>::isMatrix, int> SFINAE_Dummy = 0>
+    template <class ADummy = A, EnableMatrix<ADummy, int> = 0>
     static void addProduct(A& a, const Scalar& scalar, const B& b, const C& c) {
       sparseRangeFor(c, [&](auto&& ci, auto&& i) {
         sparseRangeFor(ci, [&](auto&& cij, auto&& j) {
@@ -398,6 +378,7 @@ namespace MatrixVector {
     }
   };
 
-}
-}
-#endif
+} // end namespace MatrixVector
+} // end namespace Dune
+
+#endif // DUNE_MATRIX_VECTOR_AXPY_HH
diff --git a/dune/matrix-vector/axy.hh b/dune/matrix-vector/axy.hh
index c626b128dd023d6a2cdfc0f06a98dd8f038cce87..016ae8a94b42d0c8a922a0e3a707c15201983a6d 100644
--- a/dune/matrix-vector/axy.hh
+++ b/dune/matrix-vector/axy.hh
@@ -3,17 +3,21 @@
 
 #include <cassert>
 
-#include "axpy.hh"
-#include "matrixtraits.hh"
-#include "algorithm.hh"
+#include <dune/matrix-vector/algorithm.hh>
+#include <dune/matrix-vector/axpy.hh>
+#include <dune/matrix-vector/traits/utilities.hh>
 
 namespace Dune {
 namespace MatrixVector {
+
   /** \brief Internal helper class for Matrix operations
    *
    */
-  template <class OperatorType, bool isMatrix>
-  struct OperatorHelper {
+  template <class T, typename Enable = void>
+  struct OperatorHelper;
+
+  template <class OperatorType>
+  struct OperatorHelper<OperatorType, DisableMatrix<OperatorType>> {
     template <class VectorType, class VectorType2>
     static typename VectorType::field_type Axy(const OperatorType &A,
                                                const VectorType &x,
@@ -36,7 +40,7 @@ namespace MatrixVector {
   };
 
   template <class MatrixType>
-  struct OperatorHelper<MatrixType, true> {
+  struct OperatorHelper<MatrixType, EnableMatrix<MatrixType>> {
     template <class VectorType, class VectorType2>
     static typename VectorType::field_type Axy(const MatrixType &A,
                                                const VectorType &x,
@@ -90,8 +94,7 @@ namespace MatrixVector {
   typename VectorType::field_type Axy(const OperatorType &A,
                                       const VectorType &x,
                                       const VectorType2 &y) {
-    return OperatorHelper<OperatorType,
-                          MatrixTraits<OperatorType>::isMatrix>::Axy(A, x, y);
+    return OperatorHelper<OperatorType>::Axy(A, x, y);
   }
 
   //! Compute \f$(b-Ax,y)\f$
@@ -100,11 +103,10 @@ namespace MatrixVector {
                                         const VectorType2 &b,
                                         const VectorType &x,
                                         const VectorType2 &y) {
-    return OperatorHelper<OperatorType,
-                          MatrixTraits<OperatorType>::isMatrix>::bmAxy(A, b, x,
-                                                                       y);
+    return OperatorHelper<OperatorType>::bmAxy(A, b, x, y);
   }
-}
-}
 
-#endif
+} // end namespace MatrixVector
+} // end namespace Dune
+
+#endif // DUNE_MATRIX_VECTOR_AXY_HH
diff --git a/dune/matrix-vector/genericvectortools.hh b/dune/matrix-vector/genericvectortools.hh
index 9b29545930305792d4b9c9bb242e284662c8d5fb..62bf76d337cf49e5610df237eff21e8997211b30 100644
--- a/dune/matrix-vector/genericvectortools.hh
+++ b/dune/matrix-vector/genericvectortools.hh
@@ -9,14 +9,11 @@
 #include <iostream>
 #include <vector>
 
-#include <dune/common/classname.hh>
-#include <dune/common/concept.hh>
 #include <dune/common/fvector.hh>
 #include <dune/common/hybridutilities.hh>
-#include <dune/common/typetraits.hh>
 
 #include <dune/matrix-vector/algorithm.hh>
-#include <dune/matrix-vector/matrixtraits.hh>
+#include <dune/matrix-vector/traits/utilities.hh>
 
 //! \brief Various tools for working with istl vectors of arbitrary nesting depth
 namespace Dune {
@@ -51,8 +48,7 @@ namespace Impl {
 
 //! recursion helper for scalars nested in iterables (vectors)
 template <class Vector>
-struct ScalarSwitch<Vector,
-                    typename std::enable_if_t<not IsNumber<Vector>::value>> {
+struct ScalarSwitch<Vector, DisableNumber<Vector>> {
 
   static void writeBinary(std::ostream& s, const Vector& v) {
     Hybrid::forEach(v, [&s](auto&& vi) { Generic::writeBinary(s, vi); });
@@ -72,8 +68,7 @@ struct ScalarSwitch<Vector,
 
 //! recursion anchors for scalars
 template <class Scalar>
-struct ScalarSwitch<Scalar,
-                    typename std::enable_if_t<IsNumber<Scalar>::value>> {
+struct ScalarSwitch<Scalar, EnableNumber<Scalar>> {
 
   static void writeBinary(std::ostream& s, const Scalar& v) {
     s.write(reinterpret_cast<const char*>(&v), sizeof(Scalar));
diff --git a/dune/matrix-vector/resize.hh b/dune/matrix-vector/resize.hh
index 41ec988465709636321835f112575b7333cf9e94..95c77e6d74a0c3ac5c699cb69c4aee41d808d20e 100644
--- a/dune/matrix-vector/resize.hh
+++ b/dune/matrix-vector/resize.hh
@@ -12,8 +12,7 @@
 
 #include <dune/matrix-vector/algorithm.hh>
 #include <dune/matrix-vector/concepts.hh>
-#include <dune/matrix-vector/matrixtraits.hh>
-#include <dune/matrix-vector/traitutilities.hh>
+#include <dune/matrix-vector/traits/utilities.hh>
 
 namespace Dune {
 namespace MatrixVector {
diff --git a/dune/matrix-vector/test/resizetest.cc b/dune/matrix-vector/test/resizetest.cc
index 59bfc291a7f499a7ae4153660abb95db85204490..bdb6923b1d7a5a7bf455c74cfe611894867a914d 100644
--- a/dune/matrix-vector/test/resizetest.cc
+++ b/dune/matrix-vector/test/resizetest.cc
@@ -17,7 +17,6 @@
 #include <dune/matrix-vector/algorithm.hh>
 #include <dune/matrix-vector/resize.hh>
 
-
 /// custom multitype types to allow for BlockVector nesting
 template <class... Args>
 struct CustomMultiTypeBlockVector : public Dune::MultiTypeBlockVector<Args...> {
@@ -28,19 +27,19 @@ struct CustomMultiTypeBlockMatrix : public Dune::MultiTypeBlockMatrix<Args...> {
   constexpr static int blocklevel = 1; // fake value
 };
 // inject matrix traits for CustomMultiTypeBlockMatrix
-namespace Dune { namespace MatrixVector {
+namespace Dune { namespace MatrixVector { namespace Traits {
   template <class... Args>
   struct MatrixTraits<CustomMultiTypeBlockMatrix<Args...>> {
     constexpr static bool isMatrix = true;
   };
-}}
+}}}
 // inject vector identification trait for CustomMultiTypeBlockVector
-namespace Dune { namespace MatrixVector {
+namespace Dune { namespace MatrixVector { namespace Traits {
   template <class... Args>
   struct VectorTraits<CustomMultiTypeBlockVector<Args...>> {
     constexpr static bool isVector = true;
   };
-}}
+}}}
 
 
 class ResizeTestSuite {
diff --git a/dune/matrix-vector/transformmatrix.hh b/dune/matrix-vector/transformmatrix.hh
index 3a81411771a92e59069b6aaaac38ebadf4476539..35df78280e82f98eec1b277dfeb97f54f19e9ab9 100644
--- a/dune/matrix-vector/transformmatrix.hh
+++ b/dune/matrix-vector/transformmatrix.hh
@@ -3,11 +3,12 @@
 
 #include <dune/common/diagonalmatrix.hh>
 #include <dune/common/fmatrix.hh>
+
 #include <dune/istl/matrixindexset.hh>
 #include <dune/istl/scaledidmatrix.hh>
 
-#include "axpy.hh"
-#include "scalartraits.hh"
+#include <dune/matrix-vector/axpy.hh>
+#include <dune/matrix-vector/traits/utilities.hh>
 
 namespace Dune {
 namespace MatrixVector {
@@ -255,12 +256,8 @@ namespace MatrixVector {
                             const MatrixB& B, const TransformationMatrix2& T2) {
     TransformMatrixHelper<
         MatrixA, TransformationMatrix1, MatrixB, TransformationMatrix2,
-        ScalarTraits<MatrixA>::isScalar,
-        ScalarTraits<TransformationMatrix1>::isScalar,
-        ScalarTraits<MatrixB>::isScalar,
-        ScalarTraits<
-            TransformationMatrix2>::isScalar>::addTransformedMatrix(A, T1, B,
-                                                                    T2);
+        isScalar<MatrixA>(), isScalar<TransformationMatrix1>(), isScalar<MatrixB>(),
+        isScalar<TransformationMatrix2>()>::addTransformedMatrix(A, T1, B, T2);
   }
 
   template <class MatrixA, class TransformationMatrix1, class MatrixB,
@@ -270,12 +267,8 @@ namespace MatrixVector {
     A = 0;
     TransformMatrixHelper<
         MatrixA, TransformationMatrix1, MatrixB, TransformationMatrix2,
-        ScalarTraits<MatrixA>::isScalar,
-        ScalarTraits<TransformationMatrix1>::isScalar,
-        ScalarTraits<MatrixB>::isScalar,
-        ScalarTraits<
-            TransformationMatrix2>::isScalar>::addTransformedMatrix(A, T1, B,
-                                                                    T2);
+        isScalar<MatrixA>(), isScalar<TransformationMatrix1>(), isScalar<MatrixB>(),
+        isScalar<TransformationMatrix2>()>::addTransformedMatrix(A, T1, B, T2);
   }
 
   template <class MatrixBlockA, class TransformationMatrix1, class MatrixB,