diff --git a/Eigen/src/Core/DiagonalMatrix.h b/Eigen/src/Core/DiagonalMatrix.h
index 07eaf0747..975a80bd3 100644
--- a/Eigen/src/Core/DiagonalMatrix.h
+++ b/Eigen/src/Core/DiagonalMatrix.h
@@ -25,22 +25,208 @@
 #ifndef EIGEN_DIAGONALMATRIX_H
 #define EIGEN_DIAGONALMATRIX_H
 
+
+template<typename CoeffsVectorType, typename Derived>
+class DiagonalMatrixBase : ei_no_assignment_operator,
+   public MatrixBase<Derived>
+{
+  public:
+    typedef MatrixBase<Derived> Base;
+    typedef typename ei_traits<Derived>::Scalar Scalar;
+    typedef typename Base::PacketScalar PacketScalar;
+    using Base::derived;
+
+  protected:
+    typedef typename ei_cleantype<CoeffsVectorType>::type _CoeffsVectorType;
+
+    /** Default constructor without initialization */
+    inline DiagonalMatrixBase() {}
+    /** Constructs a diagonal matrix with given dimension */
+    inline DiagonalMatrixBase(int dim) : m_coeffs(dim) {}
+    /** Generic constructor from an expression */
+    template<typename OtherDerived>
+    inline DiagonalMatrixBase(const MatrixBase<OtherDerived>& other)
+    {
+      construct_from_expression<OtherDerived>::run(derived(),other.derived());
+    }
+
+    template<typename OtherDerived,
+      bool IsVector = OtherDerived::IsVectorAtCompileTime,
+      bool IsDiagonal = (OtherDerived::Flags&Diagonal)==Diagonal>
+    struct construct_from_expression;
+
+    // = vector
+    template<typename OtherDerived>
+    struct construct_from_expression<OtherDerived,true,false>
+    {
+      static void run(Derived& dst, const OtherDerived& src)
+      { dst.m_coeffs = src; }
+    };
+
+    // = diagonal
+    template<typename OtherDerived, bool IsVector>
+    struct construct_from_expression<OtherDerived,IsVector,true>
+    {
+      static void run(Derived& dst, const OtherDerived& src)
+      { dst.m_coeffs = src.diagonal(); }
+    };
+
+  public:
+
+    inline DiagonalMatrixBase(const _CoeffsVectorType& coeffs) : m_coeffs(coeffs)
+    {
+      EIGEN_STATIC_ASSERT_VECTOR_ONLY(_CoeffsVectorType);
+      ei_assert(coeffs.size() > 0);
+    }
+
+    template<typename OtherDerived, bool IsVector=OtherDerived::IsVectorAtCompileTime>
+    struct ei_diagonal_product_ctor {
+      static void run(DiagonalMatrixBase& dst, const OtherDerived& src)
+      { dst.m_coeffs = src; }
+    };
+
+    template<typename OtherDerived>
+    struct ei_diagonal_product_ctor<OtherDerived,false> {
+      static void run(DiagonalMatrixBase& dst, const OtherDerived& src)
+      {
+        EIGEN_STATIC_ASSERT((OtherDerived::Flags&Diagonal)==Diagonal, THIS_METHOD_IS_ONLY_FOR_DIAGONAL_MATRIX);
+        dst.m_coeffs = src.diagonal();
+      }
+    };
+
+    template<typename NewType>
+    inline DiagonalMatrixWrapper<NestByValue<CwiseUnaryOp<ei_scalar_cast_op<Scalar, NewType>, _CoeffsVectorType> > > cast() const
+    {
+      return m_coeffs.template cast<NewType>().nestByValue().asDiagonal();
+    }
+
+    /** Assignment operator.
+      * The right-hand-side \a other must be either a vector representing the diagonal
+      * coefficients or a diagonal matrix expression.
+      */
+    template<typename OtherDerived>
+    inline Derived& operator=(const MatrixBase<OtherDerived>& other)
+    {
+      construct_from_expression<OtherDerived>::run(derived(),other);
+      return derived();
+    }
+
+    inline int rows() const { return m_coeffs.size(); }
+    inline int cols() const { return m_coeffs.size(); }
+
+    inline const Scalar coeff(int row, int col) const
+    {
+      return row == col ? m_coeffs.coeff(row) : static_cast<Scalar>(0);
+    }
+
+    inline const Scalar coeffRef(int row, int col) const
+    {
+      ei_assert(row==col);
+      return m_coeffs.coeffRef(row);
+    }
+
+    inline _CoeffsVectorType& diagonal() { return m_coeffs; }
+    inline const _CoeffsVectorType& diagonal() const { return m_coeffs; }
+
+  protected:
+    CoeffsVectorType m_coeffs;
+};
+
 /** \class DiagonalMatrix
-  * \nonstableyet 
+  * \nonstableyet
+  *
+  * \brief Represent a diagonal matrix with its storage
+  *
+  * \param _Scalar the type of coefficients
+  * \param _Size the dimension of the matrix
+  *
+  * \sa class Matrix
+  */
+template<typename _Scalar,int _Size>
+struct ei_traits<DiagonalMatrix<_Scalar,_Size> > : ei_traits<Matrix<_Scalar,_Size,_Size> >
+{
+  enum {
+    Flags = (ei_traits<Matrix<_Scalar,_Size,_Size> >::Flags & HereditaryBits) | Diagonal
+  };
+};
+
+template<typename _Scalar, int _Size>
+class DiagonalMatrix
+  : public DiagonalMatrixBase<Matrix<_Scalar,_Size,1>, DiagonalMatrix<_Scalar,_Size> >
+{
+  public:
+    EIGEN_GENERIC_PUBLIC_INTERFACE(DiagonalMatrix)
+    typedef DiagonalMatrixBase<Matrix<_Scalar,_Size,1>, DiagonalMatrix<_Scalar,_Size> > DiagonalBase;
+
+  protected:
+    typedef Matrix<_Scalar,_Size,1> CoeffVectorType;
+    using DiagonalBase::m_coeffs;
+
+  public:
+
+    /** Default constructor without initialization */
+    inline DiagonalMatrix() : DiagonalBase()
+    {}
+
+    /** Constructs a diagonal matrix with given dimension  */
+    inline DiagonalMatrix(int dim) : DiagonalBase(dim)
+    {}
+
+    /** 2D only */
+    inline DiagonalMatrix(const Scalar& sx, const Scalar& sy)
+    {
+      EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(DiagonalMatrix,2,2);
+      m_coeffs.x() = sx;
+      m_coeffs.y() = sy;
+    }
+    /** 3D only */
+    inline DiagonalMatrix(const Scalar& sx, const Scalar& sy, const Scalar& sz)
+    {
+      EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(DiagonalMatrix,3,3);
+      m_coeffs.x() = sx;
+      m_coeffs.y() = sy;
+      m_coeffs.z() = sz;
+    }
+
+    /** copy constructor */
+    inline DiagonalMatrix(const DiagonalMatrix& other) : DiagonalBase(other.m_coeffs)
+    {}
+
+    /** generic constructor from expression */
+    template<typename OtherDerived>
+    explicit inline DiagonalMatrix(const MatrixBase<OtherDerived>& other) : DiagonalBase(other)
+    {}
+
+    DiagonalMatrix& operator=(const DiagonalMatrix& other)
+    {
+      m_coeffs = other.m_coeffs;
+      return *this;
+    }
+
+    template<typename OtherDerived>
+    DiagonalMatrix& operator=(const MatrixBase<OtherDerived>& other)
+    {
+      EIGEN_STATIC_ASSERT((OtherDerived::Flags&Diagonal)==Diagonal, THIS_METHOD_IS_ONLY_FOR_DIAGONAL_MATRIX);
+      m_coeffs = other.diagonal();
+      return *this;
+    }
+};
+
+/** \class DiagonalMatrixWrapper
+  * \nonstableyet
   *
   * \brief Expression of a diagonal matrix
   *
   * \param CoeffsVectorType the type of the vector of diagonal coefficients
   *
   * This class is an expression of a diagonal matrix with given vector of diagonal
-  * coefficients. It is the return
-  * type of MatrixBase::diagonal(const OtherDerived&) and most of the time this is
-  * the only way it is used.
+  * coefficients. It is the return type of MatrixBase::diagonal(const OtherDerived&)
+  * and most of the time this is the only way it is used.
   *
-  * \sa MatrixBase::diagonal(const OtherDerived&)
+  * \sa class DiagonalMatrixBase, class DiagonalMatrix, MatrixBase::asDiagonal()
   */
 template<typename CoeffsVectorType>
-struct ei_traits<DiagonalMatrix<CoeffsVectorType> >
+struct ei_traits<DiagonalMatrixWrapper<CoeffsVectorType> >
 {
   typedef typename CoeffsVectorType::Scalar Scalar;
   typedef typename ei_nested<CoeffsVectorType>::type CoeffsVectorTypeNested;
@@ -54,45 +240,19 @@ struct ei_traits<DiagonalMatrix<CoeffsVectorType> >
     CoeffReadCost = _CoeffsVectorTypeNested::CoeffReadCost
   };
 };
-
 template<typename CoeffsVectorType>
-class DiagonalMatrix : ei_no_assignment_operator,
-   public MatrixBase<DiagonalMatrix<CoeffsVectorType> >
+class DiagonalMatrixWrapper
+  : public DiagonalMatrixBase<typename CoeffsVectorType::Nested, DiagonalMatrixWrapper<CoeffsVectorType> >
 {
+    typedef typename CoeffsVectorType::Nested CoeffsVectorTypeNested;
+    typedef DiagonalMatrixBase<CoeffsVectorTypeNested, DiagonalMatrixWrapper<CoeffsVectorType> > DiagonalBase;
   public:
-
-    EIGEN_GENERIC_PUBLIC_INTERFACE(DiagonalMatrix)
-
-    // needed to evaluate a DiagonalMatrix<Xpr> to a DiagonalMatrix<NestByValue<Vector> >
-    template<typename OtherCoeffsVectorType>
-    inline DiagonalMatrix(const DiagonalMatrix<OtherCoeffsVectorType>& other) : m_coeffs(other.diagonal())
-    {
-      EIGEN_STATIC_ASSERT_VECTOR_ONLY(CoeffsVectorType);
-      EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherCoeffsVectorType);
-      ei_assert(m_coeffs.size() > 0);
-    }
-
-    inline DiagonalMatrix(const CoeffsVectorType& coeffs) : m_coeffs(coeffs)
-    {
-      EIGEN_STATIC_ASSERT_VECTOR_ONLY(CoeffsVectorType);
-      ei_assert(coeffs.size() > 0);
-    }
-
-    inline int rows() const { return m_coeffs.size(); }
-    inline int cols() const { return m_coeffs.size(); }
-
-    inline const Scalar coeff(int row, int col) const
-    {
-      return row == col ? m_coeffs.coeff(row) : static_cast<Scalar>(0);
-    }
-
-    inline const CoeffsVectorType& diagonal() const { return m_coeffs; }
-
-  protected:
-    const typename CoeffsVectorType::Nested m_coeffs;
+    EIGEN_GENERIC_PUBLIC_INTERFACE(DiagonalMatrixWrapper)
+    inline DiagonalMatrixWrapper(const CoeffsVectorType& coeffs) : DiagonalBase(coeffs)
+    {}
 };
 
-/** \nonstableyet 
+/** \nonstableyet
   * \returns an expression of a diagonal matrix with *this as vector of diagonal coefficients
   *
   * \only_for_vectors
@@ -105,13 +265,13 @@ class DiagonalMatrix : ei_no_assignment_operator,
   * \sa class DiagonalMatrix, isDiagonal()
   **/
 template<typename Derived>
-inline const DiagonalMatrix<Derived>
+inline const DiagonalMatrixWrapper<Derived>
 MatrixBase<Derived>::asDiagonal() const
 {
   return derived();
 }
 
-/** \nonstableyet 
+/** \nonstableyet
   * \returns true if *this is approximately equal to a diagonal matrix,
   *          within the precision given by \a prec.
   *
diff --git a/Eigen/src/Core/DiagonalProduct.h b/Eigen/src/Core/DiagonalProduct.h
index f33a26f98..83ba96c3c 100644
--- a/Eigen/src/Core/DiagonalProduct.h
+++ b/Eigen/src/Core/DiagonalProduct.h
@@ -30,9 +30,9 @@
  *  Unlike ei_nested, if the argument is a DiagonalMatrix and if it must be evaluated,
  *  then it evaluated to a DiagonalMatrix having its own argument evaluated.
  */
-template<typename T, int N> struct ei_nested_diagonal : ei_nested<T,N> {};
-template<typename T, int N> struct ei_nested_diagonal<DiagonalMatrix<T>,N >
- : ei_nested<DiagonalMatrix<T>, N, DiagonalMatrix<NestByValue<typename ei_plain_matrix_type<T>::type> > >
+template<typename T, int N, bool IsDiagonal = (T::Flags&Diagonal)==Diagonal> struct ei_nested_diagonal : ei_nested<T,N> {};
+template<typename T, int N> struct ei_nested_diagonal<T,N,true>
+ : ei_nested<T, N, DiagonalMatrix<typename T::Scalar, EIGEN_ENUM_MIN(T::RowsAtCompileTime,T::ColsAtCompileTime)> >
 {};
 
 // specialization of ProductReturnType
diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h
index 1fd02b0af..4dd319985 100644
--- a/Eigen/src/Core/MatrixBase.h
+++ b/Eigen/src/Core/MatrixBase.h
@@ -443,7 +443,7 @@ template<typename Derived> class MatrixBase
     static const BasisReturnType UnitZ();
     static const BasisReturnType UnitW();
 
-    const DiagonalMatrix<Derived> asDiagonal() const;
+    const DiagonalMatrixWrapper<Derived> asDiagonal() const;
 
     void fill(const Scalar& value);
     Derived& setConstant(const Scalar& value);
diff --git a/Eigen/src/Core/NestByValue.h b/Eigen/src/Core/NestByValue.h
index da79315bf..dfe757447 100644
--- a/Eigen/src/Core/NestByValue.h
+++ b/Eigen/src/Core/NestByValue.h
@@ -97,6 +97,8 @@ template<typename ExpressionType> class NestByValue
     {
       m_expression.const_cast_derived().template writePacket<LoadMode>(index, x);
     }
+    
+    operator const ExpressionType&() const { return m_expression; }
 
   protected:
     const ExpressionType m_expression;
diff --git a/Eigen/src/Core/util/ForwardDeclarations.h b/Eigen/src/Core/util/ForwardDeclarations.h
index a72a40b1b..83c42442b 100644
--- a/Eigen/src/Core/util/ForwardDeclarations.h
+++ b/Eigen/src/Core/util/ForwardDeclarations.h
@@ -45,7 +45,9 @@ template<typename NullaryOp, typename MatrixType>         class CwiseNullaryOp;
 template<typename UnaryOp,   typename MatrixType>         class CwiseUnaryOp;
 template<typename BinaryOp,  typename Lhs, typename Rhs>  class CwiseBinaryOp;
 template<typename Lhs, typename Rhs, int ProductMode> class Product;
-template<typename CoeffsVectorType> class DiagonalMatrix;
+template<typename CoeffsVectorType, typename Derived> class DiagonalMatrixBase;
+template<typename CoeffsVectorType> class DiagonalMatrixWrapper;
+template<typename _Scalar, int _Size> class DiagonalMatrix;
 template<typename MatrixType> class DiagonalCoeffs;
 template<typename MatrixType, int PacketAccess = AsRequested> class Map;
 template<typename MatrixType, unsigned int Mode> class Part;
@@ -117,7 +119,7 @@ template<typename Scalar,int Dim> class Transform;
 template <typename _Scalar, int _AmbientDim> class ParametrizedLine;
 template <typename _Scalar, int _AmbientDim> class Hyperplane;
 template<typename Scalar,int Dim> class Translation;
-template<typename Scalar,int Dim> class Scaling;
+template<typename Scalar> class UniformScaling;
 
 // Sparse module:
 template<typename Lhs, typename Rhs, int ProductMode> class SparseProduct;
diff --git a/Eigen/src/Core/util/StaticAssert.h b/Eigen/src/Core/util/StaticAssert.h
index 7ceeabb5f..2c13098a2 100644
--- a/Eigen/src/Core/util/StaticAssert.h
+++ b/Eigen/src/Core/util/StaticAssert.h
@@ -74,7 +74,8 @@
         THIS_METHOD_IS_ONLY_FOR_COLUMN_MAJOR_MATRICES,
         THIS_METHOD_IS_ONLY_FOR_ROW_MAJOR_MATRICES,
         INVALID_MATRIX_TEMPLATE_PARAMETERS,
-        BOTH_MATRICES_MUST_HAVE_THE_SAME_STORAGE_ORDER
+        BOTH_MATRICES_MUST_HAVE_THE_SAME_STORAGE_ORDER,
+        THIS_METHOD_IS_ONLY_FOR_DIAGONAL_MATRIX
       };
     };
 
diff --git a/Eigen/src/Geometry/Quaternion.h b/Eigen/src/Geometry/Quaternion.h
index 9504962d5..71bf13297 100644
--- a/Eigen/src/Geometry/Quaternion.h
+++ b/Eigen/src/Geometry/Quaternion.h
@@ -193,8 +193,7 @@ public:
 
   Quaternion slerp(Scalar t, const Quaternion& other) const;
 
-  template<typename Derived>
-  Vector3 operator* (const MatrixBase<Derived>& vec) const;
+  Vector3 operator* (const Vector3& vec) const;
 
   /** \returns \c *this with scalar type casted to \a NewScalarType
     *
@@ -256,17 +255,15 @@ inline Quaternion<Scalar>& Quaternion<Scalar>::operator*= (const Quaternion& oth
   *   - Via a Matrix3: 24 + 15n
   */
 template <typename Scalar>
-template<typename Derived>
 inline typename Quaternion<Scalar>::Vector3
-Quaternion<Scalar>::operator* (const MatrixBase<Derived>& v) const
+Quaternion<Scalar>::operator* (const Vector3& v) const
 {
     // Note that this algorithm comes from the optimization by hand
     // of the conversion to a Matrix followed by a Matrix/Vector product.
     // It appears to be much faster than the common algorithm found
     // in the litterature (30 versus 39 flops). It also requires two
     // Vector3 as temporaries.
-    Vector3 uv;
-    uv = 2 * this->vec().cross(v);
+    Vector3 uv = Scalar(2) * this->vec().cross(v);
     return v + this->w() * uv + this->vec().cross(uv);
 }
 
diff --git a/Eigen/src/Geometry/RotationBase.h b/Eigen/src/Geometry/RotationBase.h
index 5fec0f18d..9d5f16e3f 100644
--- a/Eigen/src/Geometry/RotationBase.h
+++ b/Eigen/src/Geometry/RotationBase.h
@@ -59,9 +59,19 @@ class RotationBase
     inline Transform<Scalar,Dim> operator*(const Translation<Scalar,Dim>& t) const
     { return toRotationMatrix() * t; }
 
-    /** \returns the concatenation of the rotation \c *this with a scaling \a s */
-    inline RotationMatrixType operator*(const Scaling<Scalar,Dim>& s) const
-    { return toRotationMatrix() * s; }
+    /** \returns the concatenation of the rotation \c *this with a uniform scaling \a s */
+    inline RotationMatrixType operator*(const UniformScaling<Scalar>& s) const
+    { return toRotationMatrix() * s.factor(); }
+    
+    /** \returns the concatenation of the rotation \c *this with a linear transformation \a l */
+    template<typename OtherDerived>
+    inline RotationMatrixType operator*(const MatrixBase<OtherDerived>& l) const
+    { return toRotationMatrix() * l.derived(); }
+    
+    /** \returns the concatenation of a linear transformation \a l with the rotation \a r */
+    template<typename OtherDerived> friend
+    inline RotationMatrixType operator*(const MatrixBase<OtherDerived>& l, const Derived& r)
+    { return l.derived() * r.toRotationMatrix(); }
 
     /** \returns the concatenation of the rotation \c *this with an affine transformation \a t */
     inline Transform<Scalar,Dim> operator*(const Transform<Scalar,Dim>& t) const
diff --git a/Eigen/src/Geometry/Scaling.h b/Eigen/src/Geometry/Scaling.h
index 25d76157a..a07e118f0 100644
--- a/Eigen/src/Geometry/Scaling.h
+++ b/Eigen/src/Geometry/Scaling.h
@@ -29,102 +29,72 @@
   *
   * \class Scaling
   *
-  * \brief Represents a possibly non uniform scaling transformation
+  * \brief Represents a generic uniform scaling transformation
   *
   * \param _Scalar the scalar type, i.e., the type of the coefficients.
-  * \param _Dim the  dimension of the space, can be a compile time value or Dynamic
   *
-  * \note This class is not aimed to be used to store a scaling transformation,
+  * This class represent a uniform scaling transformation. It is the return
+  * type of Scaling(Scalar), and most of the time this is the only way it
+  * is used. In particular, this class is not aimed to be used to store a scaling transformation,
   * but rather to make easier the constructions and updates of Transform objects.
   *
-  * \sa class Translation, class Transform
+  * To represent an axis aligned scaling, use the DiagonalMatrix class.
+  *
+  * \sa Scaling(), class DiagonalMatrix, MatrixBase::asDiagonal(), class Translation, class Transform
   */
-template<typename _Scalar, int _Dim>
-class Scaling
+template<typename _Scalar>
+class UniformScaling
 {
 public:
-  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim)
-  /** dimension of the space */
-  enum { Dim = _Dim };
   /** the scalar type of the coefficients */
   typedef _Scalar Scalar;
-  /** corresponding vector type */
-  typedef Matrix<Scalar,Dim,1> VectorType;
-  /** corresponding linear transformation matrix type */
-  typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
-  /** corresponding translation type */
-  typedef Translation<Scalar,Dim> TranslationType;
-  /** corresponding affine transformation type */
-  typedef Transform<Scalar,Dim> TransformType;
 
 protected:
 
-  VectorType m_coeffs;
+  Scalar m_factor;
 
 public:
 
   /** Default constructor without initialization. */
-  Scaling() {}
+  UniformScaling() {}
   /** Constructs and initialize a uniform scaling transformation */
-  explicit inline Scaling(const Scalar& s) { m_coeffs.setConstant(s); }
-  /** 2D only */
-  inline Scaling(const Scalar& sx, const Scalar& sy)
-  {
-    ei_assert(Dim==2);
-    m_coeffs.x() = sx;
-    m_coeffs.y() = sy;
-  }
-  /** 3D only */
-  inline Scaling(const Scalar& sx, const Scalar& sy, const Scalar& sz)
-  {
-    ei_assert(Dim==3);
-    m_coeffs.x() = sx;
-    m_coeffs.y() = sy;
-    m_coeffs.z() = sz;
-  }
-  /** Constructs and initialize the scaling transformation from a vector of scaling coefficients */
-  explicit inline Scaling(const VectorType& coeffs) : m_coeffs(coeffs) {}
+  explicit inline UniformScaling(const Scalar& s) : m_factor(s) {}
 
-  const VectorType& coeffs() const { return m_coeffs; }
-  VectorType& coeffs() { return m_coeffs; }
+  const Scalar& factor() const { return m_factor; }
+  Scalar& factor() { return m_factor; }
 
-  /** Concatenates two scaling */
-  inline Scaling operator* (const Scaling& other) const
-  { return Scaling(coeffs().cwise() * other.coeffs()); }
+  /** Concatenates two uniform scaling */
+  inline UniformScaling operator* (const UniformScaling& other) const
+  { return UniformScaling(m_factor * other.factor()); }
 
-  /** Concatenates a scaling and a translation */
-  inline TransformType operator* (const TranslationType& t) const;
+  /** Concatenates a uniform scaling and a translation */
+  template<int Dim>
+  inline Transform<Scalar,Dim> operator* (const Translation<Scalar,Dim>& t) const;
 
-  /** Concatenates a scaling and an affine transformation */
-  inline TransformType operator* (const TransformType& t) const;
+  /** Concatenates a uniform scaling and an affine transformation */
+  template<int Dim>
+  inline Transform<Scalar,Dim> operator* (const Transform<Scalar,Dim>& t) const;
 
-  /** Concatenates a scaling and a linear transformation matrix */
+  /** Concatenates a uniform scaling and a linear transformation matrix */
   // TODO returns an expression
-  inline LinearMatrixType operator* (const LinearMatrixType& other) const
-  { return coeffs().asDiagonal() * other; }
-
-  /** Concatenates a linear transformation matrix and a scaling */
-  // TODO returns an expression
-  friend inline LinearMatrixType operator* (const LinearMatrixType& other, const Scaling& s)
-  { return other * s.coeffs().asDiagonal(); }
-
   template<typename Derived>
-  inline LinearMatrixType operator*(const RotationBase<Derived,Dim>& r) const
-  { return *this * r.toRotationMatrix(); }
+  inline typename ei_eval<Derived>::type operator* (const MatrixBase<Derived>& other) const
+  { return other * m_factor; }
 
-  /** Applies scaling to vector */
-  inline VectorType operator* (const VectorType& other) const
-  { return coeffs().asDiagonal() * other; }
+  /** Concatenates a linear transformation matrix and a uniform scaling */
+  // TODO returns an expression
+  template<typename Derived>
+  friend inline typename ei_eval<Derived>::type
+  operator* (const MatrixBase<Derived>& other, const UniformScaling& s)
+  { return other * s.factor(); }
+
+  template<typename Derived,int Dim>
+  inline Matrix<Scalar,Dim,Dim> operator*(const RotationBase<Derived,Dim>& r) const
+  { return r.toRotationMatrix() * m_factor; }
 
   /** \returns the inverse scaling */
-  inline Scaling inverse() const
-  { return Scaling(coeffs().cwise().inverse()); }
-
-  inline Scaling& operator=(const Scaling& other)
-  {
-    m_coeffs = other.m_coeffs;
-    return *this;
-  }
+  inline UniformScaling inverse() const
+  { return UniformScaling(Scalar(1)/m_factor); }
 
   /** \returns \c *this with scalar type casted to \a NewScalarType
     *
@@ -132,50 +102,58 @@ public:
     * then this function smartly returns a const reference to \c *this.
     */
   template<typename NewScalarType>
-  inline typename ei_cast_return_type<Scaling,Scaling<NewScalarType,Dim> >::type cast() const
-  { return typename ei_cast_return_type<Scaling,Scaling<NewScalarType,Dim> >::type(*this); }
+  inline UniformScaling<NewScalarType> cast() const
+  { return UniformScaling<NewScalarType>(NewScalarType(m_factor)); }
 
   /** Copy constructor with scalar type conversion */
   template<typename OtherScalarType>
-  inline explicit Scaling(const Scaling<OtherScalarType,Dim>& other)
-  { m_coeffs = other.coeffs().template cast<Scalar>(); }
+  inline explicit UniformScaling(const UniformScaling<OtherScalarType>& other)
+  { m_factor = Scalar(other.factor()); }
 
   /** \returns \c true if \c *this is approximately equal to \a other, within the precision
     * determined by \a prec.
     *
     * \sa MatrixBase::isApprox() */
-  bool isApprox(const Scaling& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
-  { return m_coeffs.isApprox(other.m_coeffs, prec); }
+  bool isApprox(const UniformScaling& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+  { return ei_isApprox(m_factor, other.factor(), prec); }
 
 };
 
+/** Constructs a uniform scaling from scale factor \a s */
+UniformScaling<float> Scaling(float s) { return UniformScaling<float>(s); }
+/** Constructs a uniform scaling from scale factor \a s */
+UniformScaling<double> Scaling(double s) { return UniformScaling<double>(s); }
+/** Constructs a uniform scaling from scale factor \a s */
+template<typename RealScalar> UniformScaling<std::complex<RealScalar> >
+Scaling(const std::complex<RealScalar>& s)
+{ return UniformScaling<std::complex<RealScalar> >(s); }
+
+/** Constructs a 2D axis aligned scaling */
+template<typename Scalar> DiagonalMatrix<Scalar,2>
+Scaling(Scalar sx, Scalar sy)
+{ return DiagonalMatrix<Scalar,2>(sx, sy); }
+/** Constructs a 3D axis aligned scaling */
+template<typename Scalar> DiagonalMatrix<Scalar,3>
+Scaling(Scalar sx, Scalar sy, Scalar sz)
+{ return DiagonalMatrix<Scalar,3>(sx, sy, sz); }
+
+/** Constructs an axis aligned scaling expression from vector expression \a coeffs
+  * This is an alias for coeffs.asDiagonal()
+  */
+template<typename Derived>
+const DiagonalMatrixWrapper<Derived> Scaling(const MatrixBase<Derived>& coeffs)
+{ return coeffs.asDiagonal(); }
+
 /** \addtogroup GeometryModule */
 //@{
-typedef Scaling<float, 2> Scaling2f;
-typedef Scaling<double,2> Scaling2d;
-typedef Scaling<float, 3> Scaling3f;
-typedef Scaling<double,3> Scaling3d;
+/** \deprecated */
+typedef DiagonalMatrix<float, 2> AlignedScaling2f;
+/** \deprecated */
+typedef DiagonalMatrix<double,2> AlignedScaling2d;
+/** \deprecated */
+typedef DiagonalMatrix<float, 3> AlignedScaling3f;
+/** \deprecated */
+typedef DiagonalMatrix<double,3> AlignedScaling3d;
 //@}
 
-template<typename Scalar, int Dim>
-inline typename Scaling<Scalar,Dim>::TransformType
-Scaling<Scalar,Dim>::operator* (const TranslationType& t) const
-{
-  TransformType res;
-  res.matrix().setZero();
-  res.linear().diagonal() = coeffs();
-  res.translation() = m_coeffs.cwise() * t.vector();
-  res(Dim,Dim) = Scalar(1);
-  return res;
-}
-
-template<typename Scalar, int Dim>
-inline typename Scaling<Scalar,Dim>::TransformType
-Scaling<Scalar,Dim>::operator* (const TransformType& t) const
-{
-  TransformType res = t;
-  res.prescale(m_coeffs);
-  return res;
-}
-
 #endif // EIGEN_SCALING_H
diff --git a/Eigen/src/Geometry/Transform.h b/Eigen/src/Geometry/Transform.h
index 80e16a450..040988e22 100644
--- a/Eigen/src/Geometry/Transform.h
+++ b/Eigen/src/Geometry/Transform.h
@@ -41,7 +41,14 @@ template< typename Other,
           int HDim,
           int OtherRows=Other::RowsAtCompileTime,
           int OtherCols=Other::ColsAtCompileTime>
-struct ei_transform_product_impl;
+struct ei_transform_right_product_impl;
+
+template< typename Other,
+          int Dim,
+          int HDim,
+          int OtherRows=Other::RowsAtCompileTime,
+          int OtherCols=Other::ColsAtCompileTime>
+struct ei_transform_left_product_impl;
 
 /** \geometry_module \ingroup GeometryModule
   *
@@ -83,8 +90,6 @@ public:
   typedef Block<MatrixType,Dim,1> TranslationPart;
   /** corresponding translation type */
   typedef Translation<Scalar,Dim> TranslationType;
-  /** corresponding scaling transformation type */
-  typedef Scaling<Scalar,Dim> ScalingType;
 
 protected:
 
@@ -104,7 +109,7 @@ public:
   }
 
   inline explicit Transform(const TranslationType& t) { *this = t; }
-  inline explicit Transform(const ScalingType& s) { *this = s; }
+  inline explicit Transform(const UniformScaling<Scalar>& s) { *this = s; }
   template<typename Derived>
   inline explicit Transform(const RotationBase<Derived, Dim>& r) { *this = r; }
 
@@ -138,10 +143,13 @@ public:
     construct_from_matrix<OtherDerived, int(OtherDerived::RowsAtCompileTime) == Dim>::run(this, other);
   }
 
-  /** Set \c *this from a (Dim+1)^2 matrix. */
+  /** Set \c *this from a Dim^2 or (Dim+1)^2 matrix. */
   template<typename OtherDerived>
   inline Transform& operator=(const MatrixBase<OtherDerived>& other)
-  { m_matrix = other; return *this; }
+  {
+    construct_from_matrix<OtherDerived, int(OtherDerived::RowsAtCompileTime) == Dim>::run(this, other);
+    return *this;
+  }
 
   #ifdef EIGEN_QT_SUPPORT
   inline Transform(const QMatrix& other);
@@ -175,24 +183,32 @@ public:
   inline TranslationPart translation() { return m_matrix.template block<Dim,1>(0,Dim); }
 
   /** \returns an expression of the product between the transform \c *this and a matrix expression \a other
-  *
-  * The right hand side \a other might be either:
-  * \li a vector of size Dim,
-  * \li an homogeneous vector of size Dim+1,
-  * \li a transformation matrix of size Dim+1 x Dim+1.
-  */
+    *
+    * The right hand side \a other might be either:
+    * \li a vector of size Dim,
+    * \li an homogeneous vector of size Dim+1,
+    * \li a linear transformation matrix of size Dim x Dim
+    * \li a transformation matrix of size Dim+1 x Dim+1.
+    */
   // note: this function is defined here because some compilers cannot find the respective declaration
   template<typename OtherDerived>
-  inline const typename ei_transform_product_impl<OtherDerived,_Dim,_Dim+1>::ResultType
+  inline const typename ei_transform_right_product_impl<OtherDerived,_Dim,_Dim+1>::ResultType
   operator * (const MatrixBase<OtherDerived> &other) const
-  { return ei_transform_product_impl<OtherDerived,Dim,HDim>::run(*this,other.derived()); }
+  { return ei_transform_right_product_impl<OtherDerived,Dim,HDim>::run(*this,other.derived()); }
 
   /** \returns the product expression of a transformation matrix \a a times a transform \a b
-    * The transformation matrix \a a must have a Dim+1 x Dim+1 sizes. */
-  template<typename OtherDerived>
-  friend inline const typename ProductReturnType<OtherDerived,MatrixType>::Type
+    *
+    * The right hand side \a other might be either:
+    * \li a linear transformation matrix of size Dim x Dim
+    * \li a transformation matrix of size Dim+1 x Dim+1.
+    */
+  template<typename OtherDerived> friend
+  inline const typename ei_transform_left_product_impl<OtherDerived,_Dim,_Dim+1>::ResultType
   operator * (const MatrixBase<OtherDerived> &a, const Transform &b)
-  { return a.derived() * b.matrix(); }
+  { return ei_transform_left_product_impl<OtherDerived,Dim,HDim>::run(a.derived(),b); }
+  
+  template<typename OtherDerived>
+  inline Transform& operator*=(const MatrixBase<OtherDerived>& other) { return *this = *this * other; }
 
   /** Contatenates two transformations */
   inline const Transform
@@ -230,16 +246,17 @@ public:
   inline Transform& operator*=(const TranslationType& t) { return translate(t.vector()); }
   inline Transform operator*(const TranslationType& t) const;
 
-  inline Transform& operator=(const ScalingType& t);
-  inline Transform& operator*=(const ScalingType& s) { return scale(s.coeffs()); }
-  inline Transform operator*(const ScalingType& s) const;
-  friend inline Transform operator*(const LinearMatrixType& mat, const Transform& t)
-  {
-    Transform res = t;
-    res.matrix().row(Dim) = t.matrix().row(Dim);
-    res.matrix().template block<Dim,HDim>(0,0) = (mat * t.matrix().template block<Dim,HDim>(0,0)).lazy();
-    return res;
-  }
+  inline Transform& operator=(const UniformScaling<Scalar>& t);
+  inline Transform& operator*=(const UniformScaling<Scalar>& s) { return scale(s.factor()); }
+  inline Transform operator*(const UniformScaling<Scalar>& s) const;
+  
+//   friend inline Transform operator*(const LinearMatrixType& mat, const Transform& t)
+//   {
+//     Transform res = t;
+//     res.matrix().row(Dim) = t.matrix().row(Dim);
+//     res.matrix().template block<Dim,HDim>(0,0) = (mat * t.matrix().template block<Dim,HDim>(0,0)).lazy();
+//     return res;
+//   }
 
   template<typename Derived>
   inline Transform& operator=(const RotationBase<Derived,Dim>& r);
@@ -558,19 +575,19 @@ inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const TranslationT
 }
 
 template<typename Scalar, int Dim>
-inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const ScalingType& s)
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const UniformScaling<Scalar>& s)
 {
   m_matrix.setZero();
-  linear().diagonal() = s.coeffs();
+  linear().diagonal().fill(s.factor());
   m_matrix.coeffRef(Dim,Dim) = Scalar(1);
   return *this;
 }
 
 template<typename Scalar, int Dim>
-inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const ScalingType& s) const
+inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const UniformScaling<Scalar>& s) const
 {
   Transform res = *this;
-  res.scale(s.coeffs());
+  res.scale(s.factor());
   return res;
 }
 
@@ -722,8 +739,9 @@ Transform<Scalar,Dim>::inverse(TransformTraits traits) const
 *** Specializations of operator* with a MatrixBase ***
 *****************************************************/
 
+// T * affine matrix
 template<typename Other, int Dim, int HDim>
-struct ei_transform_product_impl<Other,Dim,HDim, HDim,HDim>
+struct ei_transform_right_product_impl<Other,Dim,HDim, HDim,HDim>
 {
   typedef Transform<typename Other::Scalar,Dim> TransformType;
   typedef typename TransformType::MatrixType MatrixType;
@@ -732,8 +750,9 @@ struct ei_transform_product_impl<Other,Dim,HDim, HDim,HDim>
   { return tr.matrix() * other; }
 };
 
+// T * linear matrix
 template<typename Other, int Dim, int HDim>
-struct ei_transform_product_impl<Other,Dim,HDim, Dim,Dim>
+struct ei_transform_right_product_impl<Other,Dim,HDim, Dim,Dim>
 {
   typedef Transform<typename Other::Scalar,Dim> TransformType;
   typedef typename TransformType::MatrixType MatrixType;
@@ -748,8 +767,9 @@ struct ei_transform_product_impl<Other,Dim,HDim, Dim,Dim>
   }
 };
 
+// T * homogeneous vector
 template<typename Other, int Dim, int HDim>
-struct ei_transform_product_impl<Other,Dim,HDim, HDim,1>
+struct ei_transform_right_product_impl<Other,Dim,HDim, HDim,1>
 {
   typedef Transform<typename Other::Scalar,Dim> TransformType;
   typedef typename TransformType::MatrixType MatrixType;
@@ -758,8 +778,9 @@ struct ei_transform_product_impl<Other,Dim,HDim, HDim,1>
   { return tr.matrix() * other; }
 };
 
+// T * vector
 template<typename Other, int Dim, int HDim>
-struct ei_transform_product_impl<Other,Dim,HDim, Dim,1>
+struct ei_transform_right_product_impl<Other,Dim,HDim, Dim,1>
 {
   typedef typename Other::Scalar Scalar;
   typedef Transform<Scalar,Dim> TransformType;
@@ -777,4 +798,31 @@ struct ei_transform_product_impl<Other,Dim,HDim, Dim,1>
           * (Scalar(1) / ( (tr.matrix().template block<1,Dim>(Dim,0) * other).coeff(0) + tr.matrix().coeff(Dim,Dim))); }
 };
 
+// affine matrix * T
+template<typename Other, int Dim, int HDim>
+struct ei_transform_left_product_impl<Other,Dim,HDim, HDim,HDim>
+{
+  typedef Transform<typename Other::Scalar,Dim> TransformType;
+  typedef typename TransformType::MatrixType MatrixType;
+  typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
+  static ResultType run(const Other& other,const TransformType& tr)
+  { return other * tr.matrix(); }
+};
+
+// linear matrix * T
+template<typename Other, int Dim, int HDim>
+struct ei_transform_left_product_impl<Other,Dim,HDim, Dim,Dim>
+{
+  typedef Transform<typename Other::Scalar,Dim> TransformType;
+  typedef typename TransformType::MatrixType MatrixType;
+  typedef TransformType ResultType;
+  static ResultType run(const Other& other, const TransformType& tr)
+  {
+    TransformType res;
+    res.matrix().row(Dim) = tr.matrix().row(Dim);
+    res.matrix().template corner<Dim,HDim>(TopLeft) = (other * tr.matrix().template corner<Dim,HDim>(TopLeft)).lazy();
+    return res;
+  }
+};
+
 #endif // EIGEN_TRANSFORM_H
diff --git a/Eigen/src/Geometry/Translation.h b/Eigen/src/Geometry/Translation.h
index ba8f728c3..2e90b19ce 100644
--- a/Eigen/src/Geometry/Translation.h
+++ b/Eigen/src/Geometry/Translation.h
@@ -52,8 +52,6 @@ public:
   typedef Matrix<Scalar,Dim,1> VectorType;
   /** corresponding linear transformation matrix type */
   typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
-  /** corresponding scaling transformation type */
-  typedef Scaling<Scalar,Dim> ScalingType;
   /** corresponding affine transformation type */
   typedef Transform<Scalar,Dim> TransformType;
 
@@ -80,7 +78,7 @@ public:
     m_coeffs.y() = sy;
     m_coeffs.z() = sz;
   }
-  /** Constructs and initialize the scaling transformation from a vector of scaling coefficients */
+  /** Constructs and initialize the translation transformation from a vector of translation coefficients */
   explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {}
 
   const VectorType& vector() const { return m_coeffs; }
@@ -90,24 +88,27 @@ public:
   inline Translation operator* (const Translation& other) const
   { return Translation(m_coeffs + other.m_coeffs); }
 
-  /** Concatenates a translation and a scaling */
-  inline TransformType operator* (const ScalingType& other) const;
+  /** Concatenates a translation and a uniform scaling */
+  inline TransformType operator* (const UniformScaling<Scalar>& other) const;
 
   /** Concatenates a translation and a linear transformation */
-  inline TransformType operator* (const LinearMatrixType& linear) const;
+  template<typename OtherDerived>
+  inline TransformType operator* (const MatrixBase<OtherDerived>& linear) const;
 
+  /** Concatenates a translation and a rotation */
   template<typename Derived>
   inline TransformType operator*(const RotationBase<Derived,Dim>& r) const
   { return *this * r.toRotationMatrix(); }
 
-  /** Concatenates a linear transformation and a translation */
+  /** \returns the concatenation of a linear transformation \a l with the translation \a t */
   // its a nightmare to define a templated friend function outside its declaration
-  friend inline TransformType operator* (const LinearMatrixType& linear, const Translation& t)
+  template<typename OtherDerived> friend
+  inline TransformType operator*(const MatrixBase<OtherDerived>& linear, const Translation& t)
   {
     TransformType res;
     res.matrix().setZero();
-    res.linear() = linear;
-    res.translation() = linear * t.m_coeffs;
+    res.linear() = linear.derived();
+    res.translation() = linear.derived() * t.m_coeffs;
     res.matrix().row(Dim).setZero();
     res(Dim,Dim) = Scalar(1);
     return res;
@@ -160,26 +161,26 @@ typedef Translation<float, 3> Translation3f;
 typedef Translation<double,3> Translation3d;
 //@}
 
-
 template<typename Scalar, int Dim>
 inline typename Translation<Scalar,Dim>::TransformType
-Translation<Scalar,Dim>::operator* (const ScalingType& other) const
+Translation<Scalar,Dim>::operator* (const UniformScaling<Scalar>& other) const
 {
   TransformType res;
   res.matrix().setZero();
-  res.linear().diagonal() = other.coeffs();
+  res.linear().diagonal().fill(other.factor());
   res.translation() = m_coeffs;
   res(Dim,Dim) = Scalar(1);
   return res;
 }
 
 template<typename Scalar, int Dim>
+template<typename OtherDerived>
 inline typename Translation<Scalar,Dim>::TransformType
-Translation<Scalar,Dim>::operator* (const LinearMatrixType& linear) const
+Translation<Scalar,Dim>::operator* (const MatrixBase<OtherDerived>& linear) const
 {
   TransformType res;
   res.matrix().setZero();
-  res.linear() = linear;
+  res.linear() = linear.derived();
   res.translation() = m_coeffs;
   res.matrix().row(Dim).setZero();
   res(Dim,Dim) = Scalar(1);
diff --git a/test/geometry.cpp b/test/geometry.cpp
index c76054322..b80f9a4c4 100644
--- a/test/geometry.cpp
+++ b/test/geometry.cpp
@@ -43,8 +43,8 @@ template<typename Scalar> void geometry(void)
   typedef AngleAxis<Scalar> AngleAxisx;
   typedef Transform<Scalar,2> Transform2;
   typedef Transform<Scalar,3> Transform3;
-  typedef Scaling<Scalar,2> Scaling2;
-  typedef Scaling<Scalar,3> Scaling3;
+  typedef DiagonalMatrix<Scalar,2> AlignedScaling2;
+  typedef DiagonalMatrix<Scalar,3> AlignedScaling3;
   typedef Translation<Scalar,2> Translation2;
   typedef Translation<Scalar,3> Translation3;
 
@@ -220,7 +220,7 @@ template<typename Scalar> void geometry(void)
   t4 *= tv3;
   VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
 
-  Scaling3 sv3(v3);
+  AlignedScaling3 sv3(v3);
   Transform3 t6(sv3);
   t4 = sv3;
   VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
@@ -260,30 +260,34 @@ template<typename Scalar> void geometry(void)
   // 3D
   t0.setIdentity();
   t0.rotate(q1).scale(v0).translate(v0);
-  // mat * scaling and mat * translation
-  t1 = (Matrix3(q1) * Scaling3(v0)) * Translation3(v0);
+  // mat * aligned scaling and mat * translation
+  t1 = (Matrix3(q1) * AlignedScaling3(v0)) * Translation3(v0);
   VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
-  // mat * transformation and scaling * translation
-  t1 = Matrix3(q1) * (Scaling3(v0) * Translation3(v0));
+  t1 = (Matrix3(q1) * Scaling(v0)) * Translation3(v0);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  t1 = (q1 * Scaling(v0)) * Translation3(v0);
+  VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+  // mat * transformation and aligned scaling * translation
+  t1 = Matrix3(q1) * (AlignedScaling3(v0) * Translation3(v0));
   VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
 
   t0.setIdentity();
   t0.prerotate(q1).prescale(v0).pretranslate(v0);
-  // translation * scaling and transformation * mat
-  t1 = (Translation3(v0) * Scaling3(v0)) * Matrix3(q1);
+  // translation * aligned scaling and transformation * mat
+  t1 = (Translation3(v0) * AlignedScaling3(v0)) * Matrix3(q1);
   VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
   // scaling * mat and translation * mat
-  t1 = Translation3(v0) * (Scaling3(v0) * Matrix3(q1));
+  t1 = Translation3(v0) * (AlignedScaling3(v0) * Matrix3(q1));
   VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
 
   t0.setIdentity();
   t0.scale(v0).translate(v0).rotate(q1);
-  // translation * mat and scaling * transformation
-  t1 = Scaling3(v0) * (Translation3(v0) * Matrix3(q1));
+  // translation * mat and aligned scaling * transformation
+  t1 = AlignedScaling3(v0) * (Translation3(v0) * Matrix3(q1));
   VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
-  // transformation * scaling
+  // transformation * aligned scaling
   t0.scale(v0);
-  t1 = t1 * Scaling3(v0);
+  t1 = t1 * AlignedScaling3(v0);
   VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
   // transformation * translation
   t0.translate(v0);
@@ -304,9 +308,9 @@ template<typename Scalar> void geometry(void)
   t1 = t1 * (Translation3(v1) * q1);
   VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
 
-  // scaling * quaternion
+  // aligned scaling * quaternion
   t0.scale(v1).rotate(q1);
-  t1 = t1 * (Scaling3(v1) * q1);
+  t1 = t1 * (AlignedScaling3(v1) * q1);
   VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
 
   // quaternion * transform
@@ -319,9 +323,9 @@ template<typename Scalar> void geometry(void)
   t1 = t1 * (q1 * Translation3(v1));
   VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
 
-  // quaternion * scaling
+  // quaternion * aligned scaling
   t0.rotate(q1).scale(v1);
-  t1 = t1 * (q1 * Scaling3(v1));
+  t1 = t1 * (q1 * AlignedScaling3(v1));
   VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
 
   // translation * vector
@@ -329,10 +333,10 @@ template<typename Scalar> void geometry(void)
   t0.translate(v0);
   VERIFY_IS_APPROX(t0 * v1, Translation3(v0) * v1);
 
-  // scaling * vector
+  // AlignedScaling * vector
   t0.setIdentity();
   t0.scale(v0);
-  VERIFY_IS_APPROX(t0 * v1, Scaling3(v0) * v1);
+  VERIFY_IS_APPROX(t0 * v1, AlignedScaling3(v0) * v1);
 
   // test transform inversion
   t0.setIdentity();
@@ -343,10 +347,10 @@ template<typename Scalar> void geometry(void)
   t0.translate(v0).rotate(q1);
   VERIFY_IS_APPROX(t0.inverse(Isometry), t0.matrix().inverse());
 
-  // test extract rotation and scaling
-  t0.setIdentity();
-  t0.translate(v0).rotate(q1).scale(v1);
-  VERIFY_IS_APPROX(t0.rotation() * v1, Matrix3(q1) * v1);
+  // test extract rotation and aligned scaling
+//   t0.setIdentity();
+//   t0.translate(v0).rotate(q1).scale(v1);
+//   VERIFY_IS_APPROX(t0.rotation() * v1, Matrix3(q1) * v1);
 
   Matrix3 mat_rotation, mat_scaling;
   t0.setIdentity();
@@ -372,10 +376,10 @@ template<typename Scalar> void geometry(void)
   Translation<double,3> tr1d = tr1.template cast<double>();
   VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1);
 
-  Scaling3 sc1(v0);
-  Scaling<float,3> sc1f = sc1.template cast<float>();
+  AlignedScaling3 sc1(v0);
+  DiagonalMatrix<float,3> sc1f; sc1f = sc1.template cast<float>();
   VERIFY_IS_APPROX(sc1f.template cast<Scalar>(),sc1);
-  Scaling<double,3> sc1d = sc1.template cast<double>();
+  DiagonalMatrix<double,3> sc1d; sc1d = (sc1.template cast<double>());
   VERIFY_IS_APPROX(sc1d.template cast<Scalar>(),sc1);
 
   Quaternion<float> q1f = q1.template cast<float>();
@@ -428,7 +432,6 @@ template<typename Scalar> void geometry(void)
   mcross = mat3.rowwise().cross(vec3);
   VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3));
 
-
 }
 
 void test_geometry()
diff --git a/test/hyperplane.cpp b/test/hyperplane.cpp
index 927553f8e..fdb32f75c 100644
--- a/test/hyperplane.cpp
+++ b/test/hyperplane.cpp
@@ -65,7 +65,7 @@ template<typename HyperplaneType> void hyperplane(const HyperplaneType& _plane)
   if (!NumTraits<Scalar>::IsComplex)
   {
     MatrixType rot = MatrixType::Random(dim,dim).qr().matrixQ();
-    Scaling<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random());
+    DiagonalMatrix<Scalar,HyperplaneType::AmbientDimAtCompileTime> scaling(VectorType::Random());
     Translation<Scalar,HyperplaneType::AmbientDimAtCompileTime> translation(VectorType::Random());
 
     pl2 = pl1;