diff --git a/nifty/operators/diagonal_operator/diagonal_operator.py b/nifty/operators/diagonal_operator/diagonal_operator.py
index 57c0414bfcb6c6a2090c09c88d20f0a13ab75f88..a7d678ac1aa28b9181fce0ab439f866faf4ca1b5 100644
--- a/nifty/operators/diagonal_operator/diagonal_operator.py
+++ b/nifty/operators/diagonal_operator/diagonal_operator.py
@@ -105,10 +105,10 @@ class DiagonalOperator(EndomorphicOperator):
         return self._implemented
 
     @property
-    def symmetric(self):
-        if self._symmetric is None:
-            self._symmetric = (self._diagonal.val.imag == 0).all()
-        return self._symmetric
+    def self_adjoint(self):
+        if self._self_adjoint is None:
+            self._self_adjoint = (self._diagonal.val.imag == 0).all()
+        return self._self_adjoint
 
     @property
     def unitary(self):
@@ -155,8 +155,8 @@ class DiagonalOperator(EndomorphicOperator):
             # Otherwise, inplace weightening would change the external field
             f.weight(inplace=copy, power=-1)
 
-        # Reset the symmetric property:
-        self._symmetric = None
+        # Reset the self_adjoint property:
+        self._self_adjoint = None
 
         # Reset the unitarity property
         self._unitary = None
diff --git a/nifty/operators/endomorphic_operator/endomorphic_operator.py b/nifty/operators/endomorphic_operator/endomorphic_operator.py
index 897cb51e67ec4e58616334f180e6b8a9859907e8..0d9cc49cafc55636fdcb3776c572a3130e84a045 100644
--- a/nifty/operators/endomorphic_operator/endomorphic_operator.py
+++ b/nifty/operators/endomorphic_operator/endomorphic_operator.py
@@ -26,7 +26,7 @@ class EndomorphicOperator(LinearOperator):
     # ---Overwritten properties and methods---
 
     def inverse_times(self, x, spaces=None):
-        if self.symmetric and self.unitary:
+        if self.self_adjoint and self.unitary:
             return self.times(x, spaces)
         else:
             return super(EndomorphicOperator, self).inverse_times(
@@ -34,7 +34,7 @@ class EndomorphicOperator(LinearOperator):
                                                               spaces=spaces)
 
     def adjoint_times(self, x, spaces=None):
-        if self.symmetric:
+        if self.self_adjoint:
             return self.times(x, spaces)
         else:
             return super(EndomorphicOperator, self).adjoint_times(
@@ -42,7 +42,7 @@ class EndomorphicOperator(LinearOperator):
                                                                 spaces=spaces)
 
     def adjoint_inverse_times(self, x, spaces=None):
-        if self.symmetric:
+        if self.self_adjoint:
             return self.inverse_times(x, spaces)
         else:
             return super(EndomorphicOperator, self).adjoint_inverse_times(
@@ -50,7 +50,7 @@ class EndomorphicOperator(LinearOperator):
                                                                 spaces=spaces)
 
     def inverse_adjoint_times(self, x, spaces=None):
-        if self.symmetric:
+        if self.self_adjoint:
             return self.inverse_times(x, spaces)
         else:
             return super(EndomorphicOperator, self).inverse_adjoint_times(
@@ -66,5 +66,5 @@ class EndomorphicOperator(LinearOperator):
     # ---Added properties and methods---
 
     @abc.abstractproperty
-    def symmetric(self):
+    def self_adjoint(self):
         raise NotImplementedError
diff --git a/nifty/operators/projection_operator/projection_operator.py b/nifty/operators/projection_operator/projection_operator.py
index 450a65e0094d9c1a49d677bd0884dc01f48ed83b..26e49154e304fc6629b618e3ce9f4d4fe9a57ddb 100644
--- a/nifty/operators/projection_operator/projection_operator.py
+++ b/nifty/operators/projection_operator/projection_operator.py
@@ -112,5 +112,5 @@ class ProjectionOperator(EndomorphicOperator):
         return self._unitary
 
     @property
-    def symmetric(self):
+    def self_adjoint(self):
         return True
diff --git a/nifty/operators/propagator_operator/propagator_operator.py b/nifty/operators/propagator_operator/propagator_operator.py
index 2f6faa3bd996cd2d9ae379fece6ca431a01a87d5..f0ded80a41f823d25cea4de327f32ac784733888 100644
--- a/nifty/operators/propagator_operator/propagator_operator.py
+++ b/nifty/operators/propagator_operator/propagator_operator.py
@@ -79,7 +79,7 @@ class PropagatorOperator(InvertibleOperatorMixin, EndomorphicOperator):
         return True
 
     @property
-    def symmetric(self):
+    def self_adjoint(self):
         return True
 
     @property
diff --git a/nifty/operators/smoothing_operator/smoothing_operator.py b/nifty/operators/smoothing_operator/smoothing_operator.py
index a6ee75a523cbca2c171b383e63df6fba5d1bcaf6..76e5ec4b1385a54347c900f568b8878c5b73e3a7 100644
--- a/nifty/operators/smoothing_operator/smoothing_operator.py
+++ b/nifty/operators/smoothing_operator/smoothing_operator.py
@@ -58,7 +58,7 @@ class SmoothingOperator(EndomorphicOperator):
         return True
 
     @property
-    def symmetric(self):
+    def self_adjoint(self):
         return True
 
     @property