BUG: Series dot product __rmatmul__ doesn't allow matrix vector multiplication

doc/source/whatsnew/v0.24.0.txt

@@ -183,7 +183,7 @@ Offsets
 Numeric
 ^^^^^^^
 
--
+- Bug in :class:`Series` ``__rmatmul__`` doesn't support matrix vector multiplication (:issue:`21530`)
 -
 -
 

pandas/core/series.py

@@ -2066,7 +2066,7 @@ def __matmul__(self, other):
 
     def __rmatmul__(self, other):
         """ Matrix multiplication using binary `@` operator in Python>=3.5 """
-        return self.dot(other)
+        return self.dot(np.transpose(other))
 
     @Substitution(klass='Series')
     @Appender(base._shared_docs['searchsorted'])

pandas/tests/series/test_analytics.py

@@ -849,11 +849,30 @@ def test_matmul(self):
         expected = np.dot(a.values, a.values)
         assert_almost_equal(result, expected)
 
-        # np.array @ Series (__rmatmul__)
+        # GH 21530
+        # vector (1D np.array) @ Series (__rmatmul__)
         result = operator.matmul(a.values, a)
         expected = np.dot(a.values, a.values)
         assert_almost_equal(result, expected)
 
+        # GH 21530
+        # vector (1D list) @ Series (__rmatmul__)
+        result = operator.matmul(a.values.tolist(), a)
+        expected = np.dot(a.values, a.values)
+        assert_almost_equal(result, expected)
+
+        # GH 21530
+        # matrix (2D np.array) @ Series (__rmatmul__)
+        result = operator.matmul(b.T.values, a)
+        expected = np.dot(b.T.values, a.values)
+        assert_almost_equal(result, expected)
+
+        # GH 21530
+        # matrix (2D nested lists) @ Series (__rmatmul__)
+        result = operator.matmul(b.T.values.tolist(), a)
+        expected = np.dot(b.T.values, a.values)
+        assert_almost_equal(result, expected)
+
         # mixed dtype DataFrame @ Series
         a['p'] = int(a.p)
         result = operator.matmul(b.T, a)