diff --git a/phiml/math/_ops.py b/phiml/math/_ops.py
index 36231ab..80fabae 100644
--- a/phiml/math/_ops.py
+++ b/phiml/math/_ops.py
@@ -3209,7 +3209,7 @@ def close(*tensors, rel_tolerance: Union[float, Tensor] = 1e-5, abs_tolerance: U
     """
     Checks whether all tensors have equal values within the specified tolerance.
     
-    Does not check that the shapes exactly match.
+    Does not check that the shapes exactly match but if shapes are incompatible, returns `False`.
     Unlike with `always_close()`, all shapes must be compatible and tensors with different shapes are reshaped before comparing.
 
     See Also:
@@ -3233,6 +3233,8 @@ def close(*tensors, rel_tolerance: Union[float, Tensor] = 1e-5, abs_tolerance: U
     if all(t is tensors[0] for t in tensors):
         return True
     tensors = [wrap(t) for t in tensors]
+    if any(not tensors[0].shape.is_compatible(t.shape) for t in tensors[1:]):
+        return False
     c = True
     for other in tensors[1:]:
         c &= _close(tensors[0], other, rel_tolerance=rel_tolerance, abs_tolerance=abs_tolerance, equal_nan=equal_nan, reduce=reduce)
diff --git a/phiml/math/_tensors.py b/phiml/math/_tensors.py
index e20bbec..6e9cabb 100644
--- a/phiml/math/_tensors.py
+++ b/phiml/math/_tensors.py
@@ -720,6 +720,8 @@ def __rmod__(self, other):
         return self._op2(other, lambda x, y: y % x, lambda x, y: choose_backend(x, y).mod(y, x), 'rmod', '%')
 
     def __eq__(self, other) -> 'Tensor':
+        if self is other:
+            return expand(True, self.shape)
         if _EQUALITY_REDUCE[-1] == 'ref':
             return wrap(self is other)
         elif _EQUALITY_REDUCE[-1] == 'shape_and_value':
@@ -729,7 +731,10 @@ def __eq__(self, other) -> 'Tensor':
             return wrap(close(self, other, rel_tolerance=0, abs_tolerance=0))
         if other is None:
             other = float('nan')
-        return self._op2(other, lambda x, y: x == y, lambda x, y: choose_backend(x, y).equal(x, y), 'eq', '==')
+        if self.shape.is_compatible(shape(other)):
+            return self._op2(other, lambda x, y: x == y, lambda x, y: choose_backend(x, y).equal(x, y), 'eq', '==')
+        else:
+            return wrap(False)
 
     def __ne__(self, other) -> 'Tensor':
         if _EQUALITY_REDUCE[-1] == 'ref':