diff --git a/gtsam/linear/SubgraphPreconditioner.cpp b/gtsam/linear/SubgraphPreconditioner.cpp
index 9087b3c90..53ea94d6e 100644
--- a/gtsam/linear/SubgraphPreconditioner.cpp
+++ b/gtsam/linear/SubgraphPreconditioner.cpp
@@ -149,6 +149,20 @@ void SubgraphPreconditioner::multiplyInPlace(const VectorValues& y, Errors& e) c
   Ab2_.multiplyInPlace(x, ei);                  // use iterator version
 }
 
+/* ************************************************************************* */
+// Apply operator A', A'*e = [I inv(R1')*A2']*e = e1 + inv(R1')*A2'*e2
+VectorValues SubgraphPreconditioner::operator^(const Errors& e) const {
+
+  Errors::const_iterator it = e.begin();
+  VectorValues y = zero();
+  for(auto& key_value: y) {
+    key_value.second = *it;
+    ++it;
+  }
+  transposeMultiplyAdd2(1.0, it, e.end(), y);
+  return y;
+}
+
 /* ************************************************************************* */
 // y += alpha*A'*e
 void SubgraphPreconditioner::transposeMultiplyAdd
diff --git a/gtsam/linear/SubgraphPreconditioner.h b/gtsam/linear/SubgraphPreconditioner.h
index 9e005dd53..558a80bd8 100644
--- a/gtsam/linear/SubgraphPreconditioner.h
+++ b/gtsam/linear/SubgraphPreconditioner.h
@@ -125,6 +125,9 @@ namespace gtsam {
     /** Apply operator A in place: needs e allocated already */
     void multiplyInPlace(const VectorValues& y, Errors& e) const;
 
+    /** Apply operator A' */
+    VectorValues operator^(const Errors& e) const;
+
     /**
     * Add A'*e to y
     *  y += alpha*A'*[e1;e2] = [alpha*e1; alpha*inv(R1')*A2'*e2]
diff --git a/gtsam/linear/iterative.h b/gtsam/linear/iterative.h
index ff3d73801..9bd1831e9 100644
--- a/gtsam/linear/iterative.h
+++ b/gtsam/linear/iterative.h
@@ -59,6 +59,11 @@ namespace gtsam {
     /** Access b vector */
     const Vector& b() const { return b_; }
 
+    /** Apply operator A'*e */
+    Vector operator^(const Vector& e) const {
+      return A_.transpose() * e;
+    }
+
     /**
      * Print with optional string
      */