diff --git a/Eigen/src/Core/VectorwiseOp.h b/Eigen/src/Core/VectorwiseOp.h
index a88b6e736..ea0a092a5 100644
--- a/Eigen/src/Core/VectorwiseOp.h
+++ b/Eigen/src/Core/VectorwiseOp.h
@@ -173,6 +173,14 @@ struct member_redux {
   * Example: \include MatrixBase_colwise_iterator_cxx11.cpp
   * Output: \verbinclude MatrixBase_colwise_iterator_cxx11.out
   * 
+  * For a partial reduction on an empty input, some rules apply.
+  * For the sake of clarity, let's consider a vertical reduction:
+  *   - If the number of columns is zero, then a 1x0 row-major vector expression is returned.
+  *   - Otherwise, if the number of rows is zero, then
+  *       - a row vector of zeros is returned for sum-like reductions (sum, squaredNorm, norm, etc.)
+  *       - a row vector of ones is returned for a product reduction (e.g., <code>MatrixXd(n,0).colwise().prod()</code>)
+  *       - an assert is triggered for all other reductions (minCoeff,maxCoeff,redux(bin_op))
+  * 
   * \sa DenseBase::colwise(), DenseBase::rowwise(), class PartialReduxExpr
   */
 template<typename ExpressionType, int Direction> class VectorwiseOp
@@ -294,13 +302,19 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
       * The template parameter \a BinaryOp is the type of the functor
       * of the custom redux operator. Note that func must be an associative operator.
       *
+      * \warning the size along the reduction direction must be strictly positive,
+      *          otherwise an assertion is triggered.
+      * 
       * \sa class VectorwiseOp, DenseBase::colwise(), DenseBase::rowwise()
       */
     template<typename BinaryOp>
     EIGEN_DEVICE_FUNC
     const typename ReduxReturnType<BinaryOp>::Type
     redux(const BinaryOp& func = BinaryOp()) const
-    { return typename ReduxReturnType<BinaryOp>::Type(_expression(), internal::member_redux<BinaryOp,Scalar>(func)); }
+    {
+      eigen_assert(redux_length()>0 && "you are using an empty matrix");
+      return typename ReduxReturnType<BinaryOp>::Type(_expression(), internal::member_redux<BinaryOp,Scalar>(func));
+    }
 
     typedef typename ReturnType<internal::member_minCoeff>::Type MinCoeffReturnType;
     typedef typename ReturnType<internal::member_maxCoeff>::Type MaxCoeffReturnType;
@@ -325,6 +339,9 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
     /** \returns a row (or column) vector expression of the smallest coefficient
       * of each column (or row) of the referenced expression.
       *
+      * \warning the size along the reduction direction must be strictly positive,
+      *          otherwise an assertion is triggered.
+      * 
       * \warning the result is undefined if \c *this contains NaN.
       *
       * Example: \include PartialRedux_minCoeff.cpp
@@ -333,11 +350,17 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
       * \sa DenseBase::minCoeff() */
     EIGEN_DEVICE_FUNC
     const MinCoeffReturnType minCoeff() const
-    { return MinCoeffReturnType(_expression()); }
+    {
+      eigen_assert(redux_length()>0 && "you are using an empty matrix");
+      return MinCoeffReturnType(_expression());
+    }
 
     /** \returns a row (or column) vector expression of the largest coefficient
       * of each column (or row) of the referenced expression.
       *
+      * \warning the size along the reduction direction must be strictly positive,
+      *          otherwise an assertion is triggered.
+      * 
       * \warning the result is undefined if \c *this contains NaN.
       *
       * Example: \include PartialRedux_maxCoeff.cpp
@@ -346,7 +369,10 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
       * \sa DenseBase::maxCoeff() */
     EIGEN_DEVICE_FUNC
     const MaxCoeffReturnType maxCoeff() const
-    { return MaxCoeffReturnType(_expression()); }
+    {
+      eigen_assert(redux_length()>0 && "you are using an empty matrix");
+      return MaxCoeffReturnType(_expression());
+    }
 
     /** \returns a row (or column) vector expression of the squared norm
       * of each column (or row) of the referenced expression.
@@ -690,6 +716,10 @@ template<typename ExpressionType, int Direction> class VectorwiseOp
     const HNormalizedReturnType hnormalized() const;
 
   protected:
+    Index redux_length() const
+    {
+      return Direction==Vertical ? m_matrix.rows() : m_matrix.cols();
+    }
     ExpressionTypeNested m_matrix;
 };
 
diff --git a/test/vectorwiseop.cpp b/test/vectorwiseop.cpp
index 37dbcf970..4b9d2d570 100644
--- a/test/vectorwiseop.cpp
+++ b/test/vectorwiseop.cpp
@@ -134,6 +134,7 @@ template<typename MatrixType> void vectorwiseop_matrix(const MatrixType& m)
   typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType;
   typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealColVectorType;
   typedef Matrix<RealScalar, 1, MatrixType::ColsAtCompileTime> RealRowVectorType;
+  typedef Matrix<Scalar,Dynamic,Dynamic> MatrixX;
 
   Index rows = m.rows();
   Index cols = m.cols();
@@ -247,6 +248,26 @@ template<typename MatrixType> void vectorwiseop_matrix(const MatrixType& m)
   m1 = m1.rowwise() - (m1.colwise().sum()/RealScalar(m1.rows()));
   VERIFY_IS_APPROX( m1, m2 );
   VERIFY_EVALUATION_COUNT( m2 = (m1.rowwise() - m1.colwise().sum()/RealScalar(m1.rows())), (MatrixType::RowsAtCompileTime!=1 ? 1 : 0) );
+
+  // test empty expressions
+  VERIFY_IS_APPROX(m1.matrix().middleCols(0,0).rowwise().sum().eval(), MatrixX::Zero(rows,1));
+  VERIFY_IS_APPROX(m1.matrix().middleRows(0,0).colwise().sum().eval(), MatrixX::Zero(1,cols));
+  VERIFY_IS_APPROX(m1.matrix().middleCols(0,fix<0>).rowwise().sum().eval(), MatrixX::Zero(rows,1));
+  VERIFY_IS_APPROX(m1.matrix().middleRows(0,fix<0>).colwise().sum().eval(), MatrixX::Zero(1,cols));
+
+  VERIFY_IS_APPROX(m1.matrix().middleCols(0,0).rowwise().prod().eval(), MatrixX::Ones(rows,1));
+  VERIFY_IS_APPROX(m1.matrix().middleRows(0,0).colwise().prod().eval(), MatrixX::Ones(1,cols));
+  VERIFY_IS_APPROX(m1.matrix().middleCols(0,fix<0>).rowwise().prod().eval(), MatrixX::Ones(rows,1));
+  VERIFY_IS_APPROX(m1.matrix().middleRows(0,fix<0>).colwise().prod().eval(), MatrixX::Ones(1,cols));
+  
+  VERIFY_IS_APPROX(m1.matrix().middleCols(0,0).rowwise().squaredNorm().eval(), MatrixX::Zero(rows,1));
+
+  VERIFY_RAISES_ASSERT(m1.real().middleCols(0,0).rowwise().minCoeff().eval());
+  VERIFY_RAISES_ASSERT(m1.real().middleRows(0,0).colwise().maxCoeff().eval());
+  VERIFY_IS_EQUAL(m1.real().middleRows(0,0).rowwise().maxCoeff().eval().rows(),0);
+  VERIFY_IS_EQUAL(m1.real().middleCols(0,0).colwise().maxCoeff().eval().cols(),0);
+  VERIFY_IS_EQUAL(m1.real().middleRows(0,fix<0>).rowwise().maxCoeff().eval().rows(),0);
+  VERIFY_IS_EQUAL(m1.real().middleCols(0,fix<0>).colwise().maxCoeff().eval().cols(),0);
 }
 
 EIGEN_DECLARE_TEST(vectorwiseop)
@@ -256,6 +277,7 @@ EIGEN_DECLARE_TEST(vectorwiseop)
   CALL_SUBTEST_3( vectorwiseop_array(ArrayXXf(3, 4)) );
   CALL_SUBTEST_4( vectorwiseop_matrix(Matrix4cf()) );
   CALL_SUBTEST_5( vectorwiseop_matrix(Matrix4f()) );
+  CALL_SUBTEST_5( vectorwiseop_matrix(Vector4f()) );
   CALL_SUBTEST_5( vectorwiseop_matrix(Matrix<float,4,5>()) );
   CALL_SUBTEST_6( vectorwiseop_matrix(MatrixXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
   CALL_SUBTEST_7( vectorwiseop_matrix(VectorXd(internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
diff --git a/test/zerosized.cpp b/test/zerosized.cpp
index edd1f6925..6be136e25 100644
--- a/test/zerosized.cpp
+++ b/test/zerosized.cpp
@@ -16,9 +16,13 @@ template<typename MatrixType> void zeroReduction(const MatrixType& m) {
   VERIFY(!m.any());
   VERIFY(m.prod()==1);
   VERIFY(m.sum()==0);
+  VERIFY(m.norm()==0);
+  VERIFY(m.squaredNorm()==0);
   VERIFY(m.count()==0);
   VERIFY(m.allFinite());
   VERIFY(!m.hasNaN());
+  VERIFY_RAISES_ASSERT( m.minCoeff() );
+  VERIFY_RAISES_ASSERT( m.maxCoeff() );
 }