diff --git a/gtsam/geometry/SO3.cpp b/gtsam/geometry/SO3.cpp
index cd321b126..a509bcf74 100644
--- a/gtsam/geometry/SO3.cpp
+++ b/gtsam/geometry/SO3.cpp
@@ -136,7 +136,7 @@ SO3 SO3::AxisAngle(const Vector3& axis, double theta) {
 
 /* ************************************************************************* */
 SO3 SO3::ClosestTo(const Matrix3& M) {
-  Eigen::JacobiSVD<Matrix3> svd(M, Eigen::ComputeThinU | Eigen::ComputeThinV);
+  Eigen::JacobiSVD<Matrix3> svd(M, Eigen::ComputeFullU | Eigen::ComputeFullV);
   const auto& U = svd.matrixU();
   const auto& V = svd.matrixV();
   const double det = (U * V.transpose()).determinant();
diff --git a/gtsam/geometry/SOn.h b/gtsam/geometry/SOn.h
index bc6282fe4..1b5228be0 100644
--- a/gtsam/geometry/SOn.h
+++ b/gtsam/geometry/SOn.h
@@ -75,12 +75,13 @@ class SOnBase {
     Matrix G(n2, d);
     for (size_t j = 0; j < d; j++) {
       // TODO(frank): this can't be right. Think about fixed vs dynamic.
-      G.col(j) << Derived::Hat(n, Eigen::VectorXd::Unit(d, j));
+      const auto X = derived().Hat(n, Eigen::VectorXd::Unit(d, j));
+      G.col(j) = Eigen::Map<const Matrix>(X.data(), n2, 1);
     }
 
     // Vectorize
     Vector X(n2);
-    X << derived();
+    X << Eigen::Map<const Matrix>(derived().data(), n2, 1);
 
     // If requested, calculate H as (I \oplus Q) * P
     if (H) {