diff --git a/gtsam/base/Matrix.cpp b/gtsam/base/Matrix.cpp
index 1e04bc58a..6248ad77d 100644
--- a/gtsam/base/Matrix.cpp
+++ b/gtsam/base/Matrix.cpp
@@ -126,17 +126,6 @@ bool linear_dependent(const Matrix& A, const Matrix& B, double tol) {
 }
 
 /* ************************************************************************* */
-Vector operator^(const Matrix& A, const Vector & v) {
-  if (A.rows()!=v.size()) {
-    throw std::invalid_argument("Matrix operator^ : A.m(" + std::to_string(A.rows()) + ")!=v.size(" +
-                                std::to_string(v.size()) + ")");
-  }
-//  Vector vt = v.transpose();
-//  Vector vtA = vt * A;
-//  return vtA.transpose();
-  return A.transpose() * v;
-}
-
 const Eigen::IOFormat& matlabFormat() {
   static const Eigen::IOFormat matlab(
     Eigen::StreamPrecision, // precision
diff --git a/gtsam/base/Matrix.h b/gtsam/base/Matrix.h
index c8dc46ed5..2b177e3d7 100644
--- a/gtsam/base/Matrix.h
+++ b/gtsam/base/Matrix.h
@@ -132,12 +132,6 @@ GTSAM_EXPORT bool linear_independent(const Matrix& A, const Matrix& B, double to
  */
 GTSAM_EXPORT bool linear_dependent(const Matrix& A, const Matrix& B, double tol = 1e-9);
 
-/**
- * overload ^ for trans(A)*v
- * We transpose the vectors for speed.
- */
-GTSAM_EXPORT Vector operator^(const Matrix& A, const Vector & v);
-
 /** products using old-style format to improve compatibility */
 template<class MATRIX>
 inline MATRIX prod(const MATRIX& A, const MATRIX&B) {
diff --git a/gtsam/base/tests/testMatrix.cpp b/gtsam/base/tests/testMatrix.cpp
index 4c8808722..ede59a204 100644
--- a/gtsam/base/tests/testMatrix.cpp
+++ b/gtsam/base/tests/testMatrix.cpp
@@ -567,7 +567,7 @@ TEST(Matrix, matrix_vector_multiplication )
   Vector AtAv = Vector3(142., 188., 234.);
 
   EQUALITY(A*v,Av);
-  EQUALITY(A^Av,AtAv);
+  EQUALITY(A.transpose() * Av,AtAv);
 }
 
 /* ************************************************************************* */
diff --git a/gtsam/linear/iterative.h b/gtsam/linear/iterative.h
index 22f65b8de..9bd1831e9 100644
--- a/gtsam/linear/iterative.h
+++ b/gtsam/linear/iterative.h
@@ -61,7 +61,7 @@ namespace gtsam {
 
     /** Apply operator A'*e */
     Vector operator^(const Vector& e) const {
-      return A_ ^ e;
+      return A_.transpose() * e;
     }
 
     /**
@@ -71,7 +71,7 @@ namespace gtsam {
 
     /** gradient of objective function 0.5*|Ax-b_|^2 at x = A_'*(Ax-b_) */
     Vector gradient(const Vector& x) const {
-      return A() ^ (A() * x - b());
+      return A().transpose() * (A() * x - b());
     }
 
     /** Apply operator A */