diff --git a/gtsam/geometry/tests/testEssentialMatrix.cpp b/gtsam/geometry/tests/testEssentialMatrix.cpp
index 1a2965089..1901f3fb5 100644
--- a/gtsam/geometry/tests/testEssentialMatrix.cpp
+++ b/gtsam/geometry/tests/testEssentialMatrix.cpp
@@ -19,48 +19,83 @@ GTSAM_CONCEPT_MANIFOLD_INST(EssentialMatrix)
 
 //*************************************************************************
 // Create two cameras and corresponding essential matrix E
-Rot3 aRb = Rot3::yaw(M_PI_2);
-Point3 aTb(0.1, 0, 0);
+Rot3 c1Rc2 = Rot3::yaw(M_PI_2);
+Point3 c1Tc2(0.1, 0, 0);
+EssentialMatrix trueE(c1Rc2, c1Tc2);
 
 //*************************************************************************
 TEST (EssentialMatrix, equality) {
-  EssentialMatrix actual(aRb, aTb), expected(aRb, aTb);
+  EssentialMatrix actual(c1Rc2, c1Tc2), expected(c1Rc2, c1Tc2);
   EXPECT(assert_equal(expected, actual));
 }
 
 //*************************************************************************
 TEST (EssentialMatrix, retract1) {
-  EssentialMatrix expected(aRb.retract((Vector(3) << 0.1, 0, 0)), aTb);
-  EssentialMatrix trueE(aRb, aTb);
+  EssentialMatrix expected(c1Rc2.retract((Vector(3) << 0.1, 0, 0)), c1Tc2);
   EssentialMatrix actual = trueE.retract((Vector(5) << 0.1, 0, 0, 0, 0));
   EXPECT(assert_equal(expected, actual));
 }
 
 //*************************************************************************
 TEST (EssentialMatrix, retract2) {
-  EssentialMatrix expected(aRb, Sphere2(aTb).retract((Vector(2) << 0.1, 0)));
-  EssentialMatrix trueE(aRb, aTb);
+  EssentialMatrix expected(c1Rc2,
+      Sphere2(c1Tc2).retract((Vector(2) << 0.1, 0)));
   EssentialMatrix actual = trueE.retract((Vector(5) << 0, 0, 0, 0.1, 0));
   EXPECT(assert_equal(expected, actual));
 }
 
 //*************************************************************************
-Point3 transform_to_(const EssentialMatrix& E, const Point3& point) { return E.transform_to(point); }
+Point3 transform_to_(const EssentialMatrix& E, const Point3& point) {
+  return E.transform_to(point);
+}
 TEST (EssentialMatrix, transform_to) {
   // test with a more complicated EssentialMatrix
-  Rot3 aRb2 = Rot3::yaw(M_PI/3.0)*Rot3::pitch(M_PI_4)*Rot3::roll(M_PI/6.0);
+  Rot3 aRb2 = Rot3::yaw(M_PI / 3.0) * Rot3::pitch(M_PI_4)
+      * Rot3::roll(M_PI / 6.0);
   Point3 aTb2(19.2, 3.7, 5.9);
   EssentialMatrix E(aRb2, aTb2);
   //EssentialMatrix E(aRb, Sphere2(aTb).retract((Vector(2) << 0.1, 0)));
-  static Point3 P(0.2,0.7,-2);
+  static Point3 P(0.2, 0.7, -2);
   Matrix actH1, actH2;
-  E.transform_to(P,actH1,actH2);
-  Matrix expH1 = numericalDerivative21(transform_to_, E,P),
-       expH2 = numericalDerivative22(transform_to_, E,P);
+  E.transform_to(P, actH1, actH2);
+  Matrix expH1 = numericalDerivative21(transform_to_, E, P), expH2 =
+      numericalDerivative22(transform_to_, E, P);
   EXPECT(assert_equal(expH1, actH1, 1e-8));
   EXPECT(assert_equal(expH2, actH2, 1e-8));
 }
 
+//*************************************************************************
+
+/**
+ * Given essential matrix E in camera frame B, convert to body frame C
+ * @param cRb rotation from body frame to camera frame
+ * @param E essential matrix E in camera frame C
+ */
+EssentialMatrix operator*(const Rot3& cRb, const EssentialMatrix& E) {
+  Rot3 b1Rb2 = E.rotation();
+  Sphere2 b1Tb2 = E.direction();
+  Rot3  c1Rc2 = b1Rb2.conjugate(cRb);
+  Sphere2 c1Tc2 = cRb * b1Tb2;
+  return EssentialMatrix(c1Rc2, c1Tc2);
+}
+
+TEST (EssentialMatrix, rotate) {
+  // Suppose the essential matrix is specified in a body coordinate frame B
+  // which is rotated with respect to the camera frame C, via rotation bRc.
+  // The rotation between body and camera is:
+  Point3 bX(1, 0, 0), bY(0, 1, 0), bZ(0, 0, 1);
+  Rot3 bRc(bX, bZ, -bY), cRb = bRc.inverse();
+
+  // Let's compute the ground truth E in body frame:
+  Rot3 b1Rb2 = bRc * c1Rc2 * cRb;
+  Point3 b1Tb2 = bRc * c1Tc2;
+  EssentialMatrix bodyE(b1Rb2, b1Tb2);
+  EXPECT(assert_equal(bodyE, bRc * trueE, 1e-8));
+
+  // Let's go back to camera frame:
+  EXPECT(assert_equal(trueE, cRb * bodyE, 1e-8));
+}
+
 /* ************************************************************************* */
 int main() {
   TestResult tr;