diff --git a/qiskit/aqua/operators/operator_base.py b/qiskit/aqua/operators/operator_base.py
index 46bc428042..7a137ea951 100644
--- a/qiskit/aqua/operators/operator_base.py
+++ b/qiskit/aqua/operators/operator_base.py
@@ -77,14 +77,19 @@ def eval(self,
         defined to be evaluated from Zero implicitly (i.e. it is as if ``.eval('0000')`` is already
         called implicitly to always "indexing" from column 0).
 
+        If ``front`` is None, the matrix-represenation of the operator is returned.
+
         Args:
             front: The bitstring, dict of bitstrings (with values being coefficients), or
-                StateFn to evaluated by the Operator's underlying function.
+                StateFn to evaluated by the Operator's underlying function, or None.
 
         Returns:
             The output of the Operator's evaluation function. If self is a ``StateFn``, the result
             is a float or complex. If self is an Operator (``PrimitiveOp, ComposedOp, SummedOp,
-            EvolvedOp,`` etc.), the result is a StateFn. If either self or front contain proper
+            EvolvedOp,`` etc.), the result is a StateFn. 
+            If ``front`` is None, the matrix-representation of the operator is returned, which 
+            is a ``MatrixOp`` for the operators and a ``VectorStateFn`` for state-functions.
+            If either self or front contain proper
             ``ListOps`` (not ListOp subclasses), the result is an n-dimensional list of complex
             or StateFn results, resulting from the recursive evaluation by each OperatorBase
             in the ListOps.
diff --git a/qiskit/aqua/operators/primitive_ops/circuit_op.py b/qiskit/aqua/operators/primitive_ops/circuit_op.py
index 4647307ee8..48187ef33a 100644
--- a/qiskit/aqua/operators/primitive_ops/circuit_op.py
+++ b/qiskit/aqua/operators/primitive_ops/circuit_op.py
@@ -186,8 +186,8 @@ def assign_parameters(self, param_dict: dict) -> OperatorBase:
         return self.__class__(qc, coeff=param_value)
 
     def eval(self,
-             front: Union[str, dict, np.ndarray,
-                          OperatorBase] = None) -> Union[OperatorBase, float, complex]:
+             front: Optional[Union[str, Dict[str, complex], np.ndarray, OperatorBase]] = None
+             ) -> Union[OperatorBase, float, complex]:
         # pylint: disable=import-outside-toplevel
         from ..state_fns import CircuitStateFn
         from ..list_ops import ListOp
diff --git a/qiskit/aqua/operators/primitive_ops/matrix_op.py b/qiskit/aqua/operators/primitive_ops/matrix_op.py
index d860d34780..283f96cc21 100644
--- a/qiskit/aqua/operators/primitive_ops/matrix_op.py
+++ b/qiskit/aqua/operators/primitive_ops/matrix_op.py
@@ -134,8 +134,8 @@ def __str__(self) -> str:
             return "{} * {}".format(self.coeff, prim_str)
 
     def eval(self,
-             front: Union[str, dict, np.ndarray,
-                          OperatorBase] = None) -> Union[OperatorBase, float, complex]:
+             front: Optional[Union[str, Dict[str, complex], np.ndarray, OperatorBase]] = None
+             ) -> Union[OperatorBase, float, complex]:
         # For other ops' eval we return self.to_matrix_op() here, but that's unnecessary here.
         if front is None:
             return self
diff --git a/qiskit/aqua/operators/primitive_ops/pauli_op.py b/qiskit/aqua/operators/primitive_ops/pauli_op.py
index c6cf221ca8..c252086b0b 100644
--- a/qiskit/aqua/operators/primitive_ops/pauli_op.py
+++ b/qiskit/aqua/operators/primitive_ops/pauli_op.py
@@ -145,8 +145,8 @@ def __str__(self) -> str:
             return "{} * {}".format(self.coeff, prim_str)
 
     def eval(self,
-             front: Union[str, dict, np.ndarray,
-                          OperatorBase] = None) -> Union[OperatorBase, float, complex]:
+             front: Optional[Union[str, Dict[str, complex], np.ndarray, OperatorBase]] = None
+             ) -> Union[OperatorBase, float, complex]:
         if front is None:
             return self.to_matrix_op()
 
diff --git a/qiskit/aqua/operators/primitive_ops/primitive_op.py b/qiskit/aqua/operators/primitive_ops/primitive_op.py
index 043d589057..01027e0b81 100644
--- a/qiskit/aqua/operators/primitive_ops/primitive_op.py
+++ b/qiskit/aqua/operators/primitive_ops/primitive_op.py
@@ -213,8 +213,8 @@ def __repr__(self) -> str:
         return "{}({}, coeff={})".format(type(self).__name__, repr(self.primitive), self.coeff)
 
     def eval(self,
-             front: Union[str, dict, np.ndarray,
-                          OperatorBase] = None) -> Union[OperatorBase, float, complex]:
+             front: Optional[Union[str, Dict[str, complex], np.ndarray, OperatorBase]] = None
+             ) -> Union[OperatorBase, float, complex]:
         raise NotImplementedError
 
     @property
diff --git a/qiskit/aqua/operators/state_fns/circuit_state_fn.py b/qiskit/aqua/operators/state_fns/circuit_state_fn.py
index 39dd6d0e39..fedea52a3f 100644
--- a/qiskit/aqua/operators/state_fns/circuit_state_fn.py
+++ b/qiskit/aqua/operators/state_fns/circuit_state_fn.py
@@ -275,8 +275,8 @@ def assign_parameters(self, param_dict: dict) -> OperatorBase:
         return self.__class__(qc, coeff=param_value, is_measurement=self.is_measurement)
 
     def eval(self,
-             front: Union[str, dict, np.ndarray,
-                          OperatorBase] = None) -> Union[OperatorBase, float, complex]:
+             front: Optional[Union[str, Dict[str, complex], np.ndarray, OperatorBase]] = None
+             ) -> Union[OperatorBase, float, complex]:
         if front is None:
             vector_state_fn = self.to_matrix_op().eval()
             vector_state_fn = cast(OperatorBase, vector_state_fn)
diff --git a/qiskit/aqua/operators/state_fns/dict_state_fn.py b/qiskit/aqua/operators/state_fns/dict_state_fn.py
index b5ac6a4506..d060c91d87 100644
--- a/qiskit/aqua/operators/state_fns/dict_state_fn.py
+++ b/qiskit/aqua/operators/state_fns/dict_state_fn.py
@@ -182,8 +182,8 @@ def __str__(self) -> str:
 
     # pylint: disable=too-many-return-statements
     def eval(self,
-             front: Union[str, dict, np.ndarray,
-                          OperatorBase] = None) -> Union[OperatorBase, float, complex]:
+             front: Optional[Union[str, Dict[str, complex], np.ndarray, OperatorBase]] = None
+             ) -> Union[OperatorBase, float, complex]:
         if front is None:
             vector_state_fn = self.to_matrix_op().eval()
             vector_state_fn = cast(OperatorBase, vector_state_fn)
diff --git a/qiskit/aqua/operators/state_fns/state_fn.py b/qiskit/aqua/operators/state_fns/state_fn.py
index 1c03f57c2e..ea25b79161 100644
--- a/qiskit/aqua/operators/state_fns/state_fn.py
+++ b/qiskit/aqua/operators/state_fns/state_fn.py
@@ -288,8 +288,8 @@ def __repr__(self) -> str:
                                                             self.coeff, self.is_measurement)
 
     def eval(self,
-             front: Union[str, dict, np.ndarray,
-                          OperatorBase] = None) -> Union[OperatorBase, float, complex]:
+             front: Optional[Union[str, Dict[str, complex], np.ndarray, OperatorBase]] = None
+             ) -> Union[OperatorBase, float, complex]:
         raise NotImplementedError
 
     @property
diff --git a/qiskit/aqua/operators/state_fns/vector_state_fn.py b/qiskit/aqua/operators/state_fns/vector_state_fn.py
index 512fc07ccd..025a6fbed3 100644
--- a/qiskit/aqua/operators/state_fns/vector_state_fn.py
+++ b/qiskit/aqua/operators/state_fns/vector_state_fn.py
@@ -128,8 +128,8 @@ def __str__(self) -> str:
 
     # pylint: disable=too-many-return-statements
     def eval(self,
-             front: Union[str, dict, np.ndarray,
-                          OperatorBase] = None) -> Union[OperatorBase, float, complex]:
+             front: Optional[Union[str, Dict[str, complex], np.ndarray, OperatorBase]] = None
+             ) -> Union[OperatorBase, float, complex]:
         if front is None:  # this object is already a VectorStateFn
             return self