diff --git a/Eigen/src/Core/CoreEvaluators.h b/Eigen/src/Core/CoreEvaluators.h
index ec731acd5..c9b2d2d28 100644
--- a/Eigen/src/Core/CoreEvaluators.h
+++ b/Eigen/src/Core/CoreEvaluators.h
@@ -1565,50 +1565,6 @@ struct block_evaluator<ArgType, BlockRows, BlockCols, InnerPanel, /* HasDirectAc
   }
 };
 
-// -------------------- Select --------------------
-// NOTE shall we introduce a ternary_evaluator?
-
-// TODO enable vectorization for Select
-template <typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
-struct evaluator<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType>>
-    : evaluator_base<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType>> {
-  typedef Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> XprType;
-  enum {
-    CoeffReadCost = evaluator<ConditionMatrixType>::CoeffReadCost +
-                    plain_enum_max(evaluator<ThenMatrixType>::CoeffReadCost, evaluator<ElseMatrixType>::CoeffReadCost),
-
-    Flags = (unsigned int)evaluator<ThenMatrixType>::Flags & evaluator<ElseMatrixType>::Flags & HereditaryBits,
-
-    Alignment = plain_enum_min(evaluator<ThenMatrixType>::Alignment, evaluator<ElseMatrixType>::Alignment)
-  };
-
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE explicit evaluator(const XprType& select)
-      : m_conditionImpl(select.conditionMatrix()), m_thenImpl(select.thenMatrix()), m_elseImpl(select.elseMatrix()) {
-    EIGEN_INTERNAL_CHECK_COST_VALUE(CoeffReadCost);
-  }
-
-  typedef typename XprType::CoeffReturnType CoeffReturnType;
-
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index row, Index col) const {
-    if (m_conditionImpl.coeff(row, col))
-      return m_thenImpl.coeff(row, col);
-    else
-      return m_elseImpl.coeff(row, col);
-  }
-
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE CoeffReturnType coeff(Index index) const {
-    if (m_conditionImpl.coeff(index))
-      return m_thenImpl.coeff(index);
-    else
-      return m_elseImpl.coeff(index);
-  }
-
- protected:
-  evaluator<ConditionMatrixType> m_conditionImpl;
-  evaluator<ThenMatrixType> m_thenImpl;
-  evaluator<ElseMatrixType> m_elseImpl;
-};
-
 // -------------------- Replicate --------------------
 
 template <typename ArgType, int RowFactor, int ColFactor>
diff --git a/Eigen/src/Core/Select.h b/Eigen/src/Core/Select.h
index 0fa5f1e17..61a67c2f7 100644
--- a/Eigen/src/Core/Select.h
+++ b/Eigen/src/Core/Select.h
@@ -15,7 +15,7 @@
 
 namespace Eigen {
 
-/** \class Select
+/** \typedef Select
  * \ingroup Core_Module
  *
  * \brief Expression of a coefficient wise version of the C++ ternary operator ?:
@@ -24,73 +24,16 @@ namespace Eigen {
  * \tparam ThenMatrixType the type of the \em then expression
  * \tparam ElseMatrixType the type of the \em else expression
  *
- * This class represents an expression of a coefficient wise version of the C++ ternary operator ?:.
+ * This type represents an expression of a coefficient wise version of the C++ ternary operator ?:.
  * It is the return type of DenseBase::select() and most of the time this is the only way it is used.
  *
  * \sa DenseBase::select(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const
  */
-
-namespace internal {
 template <typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
-struct traits<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> > : traits<ThenMatrixType> {
-  typedef typename traits<ThenMatrixType>::Scalar Scalar;
-  typedef Dense StorageKind;
-  typedef typename traits<ThenMatrixType>::XprKind XprKind;
-  typedef typename ConditionMatrixType::Nested ConditionMatrixNested;
-  typedef typename ThenMatrixType::Nested ThenMatrixNested;
-  typedef typename ElseMatrixType::Nested ElseMatrixNested;
-  enum {
-    RowsAtCompileTime = ConditionMatrixType::RowsAtCompileTime,
-    ColsAtCompileTime = ConditionMatrixType::ColsAtCompileTime,
-    MaxRowsAtCompileTime = ConditionMatrixType::MaxRowsAtCompileTime,
-    MaxColsAtCompileTime = ConditionMatrixType::MaxColsAtCompileTime,
-    Flags = (unsigned int)ThenMatrixType::Flags & ElseMatrixType::Flags & RowMajorBit
-  };
-};
-}  // namespace internal
-
-template <typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
-class Select : public internal::dense_xpr_base<Select<ConditionMatrixType, ThenMatrixType, ElseMatrixType> >::type,
-               internal::no_assignment_operator {
- public:
-  typedef typename internal::dense_xpr_base<Select>::type Base;
-  EIGEN_DENSE_PUBLIC_INTERFACE(Select)
-
-  inline EIGEN_DEVICE_FUNC Select(const ConditionMatrixType& a_conditionMatrix, const ThenMatrixType& a_thenMatrix,
-                                  const ElseMatrixType& a_elseMatrix)
-      : m_condition(a_conditionMatrix), m_then(a_thenMatrix), m_else(a_elseMatrix) {
-    eigen_assert(m_condition.rows() == m_then.rows() && m_condition.rows() == m_else.rows());
-    eigen_assert(m_condition.cols() == m_then.cols() && m_condition.cols() == m_else.cols());
-  }
-
-  EIGEN_DEVICE_FUNC constexpr Index rows() const noexcept { return m_condition.rows(); }
-  EIGEN_DEVICE_FUNC constexpr Index cols() const noexcept { return m_condition.cols(); }
-
-  inline EIGEN_DEVICE_FUNC const Scalar coeff(Index i, Index j) const {
-    if (m_condition.coeff(i, j))
-      return m_then.coeff(i, j);
-    else
-      return m_else.coeff(i, j);
-  }
-
-  inline EIGEN_DEVICE_FUNC const Scalar coeff(Index i) const {
-    if (m_condition.coeff(i))
-      return m_then.coeff(i);
-    else
-      return m_else.coeff(i);
-  }
-
-  inline EIGEN_DEVICE_FUNC const ConditionMatrixType& conditionMatrix() const { return m_condition; }
-
-  inline EIGEN_DEVICE_FUNC const ThenMatrixType& thenMatrix() const { return m_then; }
-
-  inline EIGEN_DEVICE_FUNC const ElseMatrixType& elseMatrix() const { return m_else; }
-
- protected:
-  typename ConditionMatrixType::Nested m_condition;
-  typename ThenMatrixType::Nested m_then;
-  typename ElseMatrixType::Nested m_else;
-};
+using Select = CwiseTernaryOp<internal::scalar_boolean_select_op<typename DenseBase<ThenMatrixType>::Scalar,
+                                                                 typename DenseBase<ElseMatrixType>::Scalar,
+                                                                 typename DenseBase<ConditionMatrixType>::Scalar>,
+                              ThenMatrixType, ElseMatrixType, ConditionMatrixType>;
 
 /** \returns a matrix where each coefficient (i,j) is equal to \a thenMatrix(i,j)
  * if \c *this(i,j) != Scalar(0), and \a elseMatrix(i,j) otherwise.
@@ -98,7 +41,7 @@ class Select : public internal::dense_xpr_base<Select<ConditionMatrixType, ThenM
  * Example: \include MatrixBase_select.cpp
  * Output: \verbinclude MatrixBase_select.out
  *
- * \sa DenseBase::bitwiseSelect(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&)
+ * \sa typedef Select
  */
 template <typename Derived>
 template <typename ThenDerived, typename ElseDerived>
@@ -107,15 +50,12 @@ inline EIGEN_DEVICE_FUNC CwiseTernaryOp<
                                        typename DenseBase<Derived>::Scalar>,
     ThenDerived, ElseDerived, Derived>
 DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix, const DenseBase<ElseDerived>& elseMatrix) const {
-  using Op = internal::scalar_boolean_select_op<typename DenseBase<ThenDerived>::Scalar,
-                                                typename DenseBase<ElseDerived>::Scalar, Scalar>;
-  return CwiseTernaryOp<Op, ThenDerived, ElseDerived, Derived>(thenMatrix.derived(), elseMatrix.derived(), derived(),
-                                                               Op());
+  return Select<Derived, ThenDerived, ElseDerived>(thenMatrix.derived(), elseMatrix.derived(), derived());
 }
 /** Version of DenseBase::select(const DenseBase&, const DenseBase&) with
  * the \em else expression being a scalar value.
  *
- * \sa DenseBase::booleanSelect(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
+ * \sa typedef Select
  */
 template <typename Derived>
 template <typename ThenDerived>
@@ -126,15 +66,13 @@ inline EIGEN_DEVICE_FUNC CwiseTernaryOp<
 DenseBase<Derived>::select(const DenseBase<ThenDerived>& thenMatrix,
                            const typename DenseBase<ThenDerived>::Scalar& elseScalar) const {
   using ElseConstantType = typename DenseBase<ThenDerived>::ConstantReturnType;
-  using Op = internal::scalar_boolean_select_op<typename DenseBase<ThenDerived>::Scalar,
-                                                typename DenseBase<ThenDerived>::Scalar, Scalar>;
-  return CwiseTernaryOp<Op, ThenDerived, ElseConstantType, Derived>(
-      thenMatrix.derived(), ElseConstantType(rows(), cols(), elseScalar), derived(), Op());
+  return Select<Derived, ThenDerived, ElseConstantType>(thenMatrix.derived(),
+                                                        ElseConstantType(rows(), cols(), elseScalar), derived());
 }
 /** Version of DenseBase::select(const DenseBase&, const DenseBase&) with
  * the \em then expression being a scalar value.
  *
- * \sa DenseBase::booleanSelect(const DenseBase<ThenDerived>&, const DenseBase<ElseDerived>&) const, class Select
+ * \sa typedef Select
  */
 template <typename Derived>
 template <typename ElseDerived>
@@ -145,10 +83,8 @@ inline EIGEN_DEVICE_FUNC CwiseTernaryOp<
 DenseBase<Derived>::select(const typename DenseBase<ElseDerived>::Scalar& thenScalar,
                            const DenseBase<ElseDerived>& elseMatrix) const {
   using ThenConstantType = typename DenseBase<ElseDerived>::ConstantReturnType;
-  using Op = internal::scalar_boolean_select_op<typename DenseBase<ElseDerived>::Scalar,
-                                                typename DenseBase<ElseDerived>::Scalar, Scalar>;
-  return CwiseTernaryOp<Op, ThenConstantType, ElseDerived, Derived>(ThenConstantType(rows(), cols(), thenScalar),
-                                                                    elseMatrix.derived(), derived(), Op());
+  return Select<Derived, ThenConstantType, ElseDerived>(ThenConstantType(rows(), cols(), thenScalar),
+                                                        elseMatrix.derived(), derived());
 }
 
 }  // end namespace Eigen
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index 3c0bc461e..4eb134f36 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -397,8 +397,6 @@ template <typename Scalar_, int Rows_, int Cols_,
                                                                    : EIGEN_DEFAULT_MATRIX_STORAGE_ORDER_OPTION),
           int MaxRows_ = Rows_, int MaxCols_ = Cols_>
 class Array;
-template <typename ConditionMatrixType, typename ThenMatrixType, typename ElseMatrixType>
-class Select;
 template <typename MatrixType, typename BinaryOp, int Direction>
 class PartialReduxExpr;
 template <typename ExpressionType, int Direction>
diff --git a/test/array_cwise.cpp b/test/array_cwise.cpp
index 6ff8d67be..d37e47a64 100644
--- a/test/array_cwise.cpp
+++ b/test/array_cwise.cpp
@@ -734,7 +734,7 @@ void comparisons(const ArrayType& m) {
   VERIFY_IS_CWISE_EQUAL(m1.abs().cwiseLessOrEqual(NumTraits<Scalar>::highest()), bool_true);
   VERIFY_IS_CWISE_EQUAL(m1.abs().cwiseGreaterOrEqual(Scalar(0)), bool_true);
 
-  // test Select
+  // test select
   VERIFY_IS_APPROX((m1 < m2).select(m1, m2), m1.cwiseMin(m2));
   VERIFY_IS_APPROX((m1 > m2).select(m1, m2), m1.cwiseMax(m2));
   Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff()) / Scalar(2);
diff --git a/test/array_for_matrix.cpp b/test/array_for_matrix.cpp
index e94398a65..e8d2c7d36 100644
--- a/test/array_for_matrix.cpp
+++ b/test/array_for_matrix.cpp
@@ -120,7 +120,7 @@ void comparisons(const MatrixType& m) {
   VERIFY((m1.array() == m1(r, c)).any());
   VERIFY(m1.cwiseEqual(m1(r, c)).any());
 
-  // test Select
+  // test select
   VERIFY_IS_APPROX((m1.array() < m2.array()).select(m1, m2), m1.cwiseMin(m2));
   VERIFY_IS_APPROX((m1.array() > m2.array()).select(m1, m2), m1.cwiseMax(m2));
   Scalar mid = m1.cwiseAbs().minCoeff() / Scalar(2) + m1.cwiseAbs().maxCoeff() / Scalar(2);
diff --git a/test/evaluators.cpp b/test/evaluators.cpp
index d96a0a19c..5a4ab3764 100644
--- a/test/evaluators.cpp
+++ b/test/evaluators.cpp
@@ -340,7 +340,7 @@ EIGEN_DECLARE_TEST(evaluators) {
     matXcd_ref.imag() = mat2;
     VERIFY_IS_APPROX(matXcd, matXcd_ref);
 
-    // test Select
+    // test select
     VERIFY_IS_APPROX_EVALUATOR(aX, (aXsrc > 0).select(aXsrc, -aXsrc));
 
     // test Replicate