diff --git a/heat/core/linalg/basics.py b/heat/core/linalg/basics.py
index 53e5e94e8..2f57fe774 100644
--- a/heat/core/linalg/basics.py
+++ b/heat/core/linalg/basics.py
@@ -430,9 +430,9 @@ def matmul(a: DNDarray, b: DNDarray, allow_resplit: bool = False) -> DNDarray:
     Parameters
     -----------
     a : DNDarray
-        matrix :math:`L \\times P` or vector :math:`P` or batch of matrices/vectors: :math:`B_1 \\times ... \\times B_k [\\times L] \\times P`
+        matrix :math:`L \\times P` or vector :math:`P` or batch of matrices: :math:`B_1 \\times ... \\times B_k \\times L \\times P`
     b : DNDarray
-        matrix :math:`P \\times Q` or vector :math:`P` or batch of matrices/vectors: :math:`B_1 \\times ... \\times B_k \\times P [\\times Q]`
+        matrix :math:`P \\times Q` or vector :math:`P` or batch of matrices: :math:`B_1 \\times ... \\times B_k \\times P \\times Q`
     allow_resplit : bool, optional
         Whether to distribute ``a`` in the case that both ``a.split is None`` and ``b.split is None``.
         Default is ``False``. If ``True``, if both are not split then ``a`` will be distributed in-place along axis 0.
@@ -440,7 +440,7 @@ def matmul(a: DNDarray, b: DNDarray, allow_resplit: bool = False) -> DNDarray:
     Notes
     -----------
     - For batched inputs, batch dimensions must coincide and if one matrix is split along a batch axis the other must be split along the same axis.
-    - If ``a`` or ``b`` is a (possibly batched) vector the result will also be a (possibly batched) vector.
+    - If ``a`` or ``b`` is a vector the result will also be a vector.
     - We recommend to avoid the particular split combinations ``1``-``0``, ``None``-``0``, and ``1``-``None`` (for ``a.split``-``b.split``) due to their comparably high memory consumption, if possible. Applying ``DNDarray.resplit_`` or ``heat.resplit`` on one of the two factors before calling ``matmul`` in these situations might improve performance of your code / might avoid memory bottlenecks.
 
     References
@@ -529,6 +529,10 @@ def matmul(a: DNDarray, b: DNDarray, allow_resplit: bool = False) -> DNDarray:
             raise NotImplementedError(
                 "Both input matrices have to be split along the same batch axis!"
             )
+        if vector_flag:  # batched matrix vector multiplication not supported
+            raise NotImplementedError(
+                "Batched matrix-vector multiplication is not supported, try using expand_dims to make it a batched matrix-matrix multiplication."
+            )
 
     comm = a.comm
     ndim = max(a.ndim, b.ndim)
diff --git a/heat/core/linalg/tests/test_basics.py b/heat/core/linalg/tests/test_basics.py
index 39fc2583b..870d671f6 100644
--- a/heat/core/linalg/tests/test_basics.py
+++ b/heat/core/linalg/tests/test_basics.py
@@ -827,14 +827,16 @@ def test_matmul(self):
                 a = ht.zeros((3, 3, 3), split=0)
                 b = ht.zeros((4, 3, 3), split=0)
                 ht.matmul(a, b)
-            # not implemented split
-            """
-            todo
+            # split along different batch dimension
             with self.assertRaises(NotImplementedError):
-                a = ht.zeros((3, 3, 3))
-                b = ht.zeros((3, 3, 3))
+                a = ht.zeros((4, 3, 3, 3), split=0)
+                b = ht.zeros((4, 3, 3, 3), split=1)
+                ht.matmul(a, b)
+            # batched matrix-vector multiplication
+            with self.assertRaises(NotImplementedError):
+                a = ht.zeros((3, 3, 3), split=0)
+                b = ht.zeros((3, 3), split=0)
                 ht.matmul(a, b)
-            """
 
             # batched, split batch
             n = 11  # number of batches