diff --git a/linear_operator/operators/low_rank_root_added_diag_linear_operator.py b/linear_operator/operators/low_rank_root_added_diag_linear_operator.py
index 6e7f1aba..0622209e 100644
--- a/linear_operator/operators/low_rank_root_added_diag_linear_operator.py
+++ b/linear_operator/operators/low_rank_root_added_diag_linear_operator.py
@@ -40,7 +40,11 @@ def chol_cap_mat(self):
         V = self._linear_op.root.mT
         C = ConstantDiagLinearOperator(torch.ones(*V.batch_shape, 1, device=V.device, dtype=V.dtype), V.shape[-2])
 
-        cap_mat = to_dense(C + V.matmul(A_inv.matmul(U)))
+        if isinstance(self._diag_tensor, ConstantDiagLinearOperator):
+            sigma_inv = A_inv.diag_values[0]
+            cap_mat = to_dense(C + sigma_inv * V.matmul(U))
+        else:
+            cap_mat = to_dense(C + V.matmul(A_inv.matmul(U)))
         chol_cap_mat = psd_safe_cholesky(cap_mat)
 
         return chol_cap_mat