diff --git a/gtsam/geometry/SOt.cpp b/gtsam/geometry/SOt.cpp
index bf259041d..a5e8f457d 100644
--- a/gtsam/geometry/SOt.cpp
+++ b/gtsam/geometry/SOt.cpp
@@ -159,16 +159,25 @@ Vector3 DexpFunctor::applyInvDexp(const Vector3& v, OptionalJacobian<3, 3> H1,
 // }
 
 //******************************************************************************
-// Matrix3 SO3::Hat(const Vector3& xi) { return skewSymmetric(xi); }
+template <>
+Matrix3 SO3::Hat(const Vector3& xi) {
+  // skew symmetric matrix X = xi^
+  Matrix3 Y = Z_3x3;
+  Y(0, 1) = -xi(2);
+  Y(0, 2) = +xi(1);
+  Y(1, 2) = -xi(0);
+  return Y - Y.transpose();
+}
 
-// /* *************************************************************************
-// */ Vector3 SO3::Vee(const Matrix3& X) {
-//   Vector3 xi;
-//   xi(0) = -X(1, 2);
-//   xi(1) = X(0, 2);
-//   xi(2) = -X(0, 1);
-//   return xi;
-// }
+//******************************************************************************
+template <>
+Vector3 SO3::Vee(const Matrix3& X) {
+  Vector3 xi;
+  xi(0) = -X(1, 2);
+  xi(1) = +X(0, 2);
+  xi(2) = -X(0, 1);
+  return xi;
+}
 
 //******************************************************************************
 template <>
diff --git a/gtsam/geometry/SOt.h b/gtsam/geometry/SOt.h
index 4b62d92e3..52d000c93 100644
--- a/gtsam/geometry/SOt.h
+++ b/gtsam/geometry/SOt.h
@@ -39,12 +39,15 @@ using SO3 = SO<3>;
 //   /// Static, named constructor that finds chordal mean = argmin_R \sum
 //   sqr(|R-R_i|_F). static SO3 ChordalMean(const std::vector<SO3>& rotations);
 
-//   static Matrix3 Hat(const Vector3 &xi); ///< make skew symmetric matrix
-//   static Vector3 Vee(const Matrix3 &X);  ///< inverse of Hat
-
 // Below are all declarations of SO<3> specializations.
 // They are *defined* in SO3.cpp.
 
+template <>
+Matrix3 SO3::Hat(const Vector3& xi);  ///< make skew symmetric matrix
+
+template <>
+Vector3 SO3::Vee(const Matrix3& X);  ///< inverse of Hat
+
 /// Adjoint map
 template <>
 Matrix3 SO3::AdjointMap() const {
diff --git a/gtsam/geometry/tests/testSO3.cpp b/gtsam/geometry/tests/testSO3.cpp
index d6ca68ccf..f7a936a74 100644
--- a/gtsam/geometry/tests/testSO3.cpp
+++ b/gtsam/geometry/tests/testSO3.cpp
@@ -44,10 +44,27 @@ TEST(SO3, Constructor) { SO3 q(Eigen::AngleAxisd(1, Vector3(0, 0, 1))); }
 
 //******************************************************************************
 SO3 id;
-Vector3 z_axis(0, 0, 1);
+Vector3 z_axis(0, 0, 1), v2(1, 2, 0), v3(1, 2, 3);
 SO3 R1(Eigen::AngleAxisd(0.1, z_axis));
 SO3 R2(Eigen::AngleAxisd(0.2, z_axis));
 
+//******************************************************************************
+TEST(SO3, Hat) {
+  // Check that Hat specialization is equal to dynamic version
+  EXPECT(assert_equal(SO3::Hat(z_axis), SOn::Hat(z_axis)));
+  EXPECT(assert_equal(SO3::Hat(v2), SOn::Hat(v2)));
+  EXPECT(assert_equal(SO3::Hat(v3), SOn::Hat(v3)));
+}
+
+//******************************************************************************
+TEST(SO3, Vee) {
+  // Check that Hat specialization is equal to dynamic version
+  auto X1 = SOn::Hat(z_axis), X2 = SOn::Hat(v2), X3 = SOn::Hat(v3);
+  EXPECT(assert_equal(SO3::Vee(X1), SOn::Vee(X1)));
+  EXPECT(assert_equal(SO3::Vee(X2), SOn::Vee(X2)));
+  EXPECT(assert_equal(SO3::Vee(X3), SOn::Vee(X3)));
+}
+
 //******************************************************************************
 TEST(SO3, Local) {
   Vector3 expected(0, 0, 0.1);