diff --git a/gpytorch/kernels/linear_kernel.py b/gpytorch/kernels/linear_kernel.py
index 51936766e..10102e1be 100644
--- a/gpytorch/kernels/linear_kernel.py
+++ b/gpytorch/kernels/linear_kernel.py
@@ -52,7 +52,7 @@ def __init__(
         variance_constraint: Optional[Interval] = None,
         **kwargs,
     ):
-        super(LinearKernel, self).__init__(**kwargs)
+        super().__init__(**kwargs)
         if variance_constraint is None:
             variance_constraint = Positive()
         self.register_parameter(
@@ -73,17 +73,17 @@ def variance(self) -> Tensor:
         return self.raw_variance_constraint.transform(self.raw_variance)
 
     @variance.setter
-    def variance(self, value: Union[float, Tensor]):
+    def variance(self, value: Union[float, Tensor]) -> None:
         self._set_variance(value)
 
-    def _set_variance(self, value: Union[float, Tensor]):
+    def _set_variance(self, value: Union[float, Tensor]) -> None:
         if not torch.is_tensor(value):
             value = torch.as_tensor(value).to(self.raw_variance)
         self.initialize(raw_variance=self.raw_variance_constraint.inverse_transform(value))
 
     def forward(
-        self, x1: Tensor, x2: Tensor, diag: Optional[bool] = False, last_dim_is_batch: Optional[bool] = False, **params
-    ) -> LinearOperator:
+        self, x1: Tensor, x2: Tensor, diag: bool = False, last_dim_is_batch: Optional[bool] = False, **params
+    ) -> Union[Tensor, LinearOperator]:
         x1_ = x1 * self.variance.sqrt()
         if last_dim_is_batch:
             x1_ = x1_.transpose(-1, -2).unsqueeze(-1)