diff --git a/gtsam/base/concepts.h b/gtsam/base/concepts.h
index b7eba2635..c2c530429 100644
--- a/gtsam/base/concepts.h
+++ b/gtsam/base/concepts.h
@@ -363,9 +363,11 @@ struct traits_x<float> : public internal::ScalarTraits<float> {};
 // traits for any double Eigen matrix
 template<int M, int N, int Options, int MaxRows, int MaxCols>
 struct traits_x< Eigen::Matrix<double, M, N, Options, MaxRows, MaxCols> > {
+  BOOST_STATIC_ASSERT_MSG(M != Eigen::Dynamic && N != Eigen::Dynamic,
+      "This traits class only supports fixed-size matrices.");
   // Typedefs required by all manifold types.
   typedef vector_space_tag structure_category;
-  enum { dimension = (M == Eigen::Dynamic ? Eigen::Dynamic : (N == Eigen::Dynamic ? Eigen::Dynamic : M * N)) };
+  enum { dimension = M * N };
   typedef Eigen::Matrix<double, dimension, 1> TangentVector;
   typedef OptionalJacobian<dimension, dimension> ChartJacobian;
   typedef Eigen::Matrix<double, M, N, Options, MaxRows, MaxCols> ManifoldType;
@@ -405,8 +407,7 @@ struct traits_x< Eigen::Matrix<double, M, N, Options, MaxRows, MaxCols> > {
                               ChartJacobian Hv = boost::none) {
     if (Horigin) *Horigin = Eye(origin);
     if (Hv) *Hv = Eye(origin);
-    return origin +
-        Eigen::Map<Eigen::Matrix<double, M, N> >(v.data(), origin.rows(), origin.cols());
+    return origin + Eigen::Map<const Eigen::Matrix<double, M, N> >(v.data(), origin.rows(), origin.cols());
   }
 
   static ManifoldType Compose(const ManifoldType& m1,
@@ -444,7 +445,7 @@ struct traits_x< Eigen::Matrix<double, M, N, Options, MaxRows, MaxCols> > {
     if (Hm) *Hm = Eye(m);
     TangentVector result(GetDimension(m));
     Eigen::Map<Eigen::Matrix<double, M, N> >(
-      result.data(), m.rows(), m.cols()) = m;
+      result.data()) = m;
     return result;
   }
 
@@ -453,7 +454,7 @@ struct traits_x< Eigen::Matrix<double, M, N, Options, MaxRows, MaxCols> > {
     ManifoldType m; m.setZero();
     if (Hv) *Hv = Eye(m);
     return m +
-        Eigen::Map<Eigen::Matrix<double, M, N> >(v.data(), m.rows(), m.cols());
+        Eigen::Map<Eigen::Matrix<double, M, N> >(v.data());
   }
 
 };
diff --git a/gtsam/base/numericalDerivative.h b/gtsam/base/numericalDerivative.h
index c1ee87a26..0a783037a 100644
--- a/gtsam/base/numericalDerivative.h
+++ b/gtsam/base/numericalDerivative.h
@@ -70,7 +70,7 @@ Vector numericalGradient(boost::function<double(const X&)> h, const X& x,
   double factor = 1.0 / (2.0 * delta);
 
   BOOST_STATIC_ASSERT_MSG(
-      (boost::is_base_of<manifold_tag, typename traits_x<X>::structure_category_tag>::value),
+      (boost::is_base_of<manifold_tag, typename traits_x<X>::structure_category>::value),
       "Template argument X must be a manifold type.");
   static const int N = traits_x<X>::dimension;
   BOOST_STATIC_ASSERT_MSG(N>0, "Template argument X must be fixed-size type.");
@@ -300,10 +300,11 @@ inline Matrix numericalHessian(boost::function<double(const X&)> f, const X& x,
     double delta = 1e-5) {
   BOOST_STATIC_ASSERT_MSG( (boost::is_base_of<gtsam::manifold_tag, typename traits_x<X>::structure_category>::value),
       "Template argument X must be a manifold type.");
+  typedef Eigen::Matrix<double, traits_x<X>::dimension, 1> VectorD;
   typedef boost::function<double(const X&)> F;
-  typedef boost::function<Vector(F, const X&, double)> G;
+  typedef boost::function<VectorD(F, const X&, double)> G;
   G ng = static_cast<G>(numericalGradient<X> );
-  return numericalDerivative11<Vector, X>(boost::bind(ng, f, _1, delta), x,
+  return numericalDerivative11<VectorD, X>(boost::bind(ng, f, _1, delta), x,
       delta);
 }