BUG: fixes Arrow Dataframes/Series producing a Numpy object result (#54025)

* fix dot dtype

* missing pa fix

* fix doc build issue

* expand tests

* fix win dtype

* update

* Update doc/source/whatsnew/v2.1.0.rst

Co-authored-by: Matthew Roeschke <10647082+mroeschke@users.noreply.github.com>

---------

Co-authored-by: Matthew Roeschke <10647082+mroeschke@users.noreply.github.com>

Author: mcgeestocks

doc/source/whatsnew/v2.1.0.rst

@@ -467,6 +467,7 @@ Numeric
 - Bug in :meth:`Series.mean`, :meth:`DataFrame.mean` with object-dtype values containing strings that can be converted to numbers (e.g. "2") returning incorrect numeric results; these now raise ``TypeError`` (:issue:`36703`, :issue:`44008`)
 - Bug in :meth:`DataFrame.corrwith` raising ``NotImplementedError`` for pyarrow-backed dtypes (:issue:`52314`)
 - Bug in :meth:`DataFrame.size` and :meth:`Series.size` returning 64-bit integer instead of int (:issue:`52897`)
+- Bug in :meth:`DateFrame.dot` returning ``object`` dtype for :class:`ArrowDtype` data (:issue:`53979`)
 - Bug in :meth:`Series.any`, :meth:`Series.all`, :meth:`DataFrame.any`, and :meth:`DataFrame.all` had the default value of ``bool_only`` set to ``None`` instead of ``False``; this change should have no impact on users (:issue:`53258`)
 - Bug in :meth:`Series.corr` and :meth:`Series.cov` raising ``AttributeError`` for masked dtypes (:issue:`51422`)
 - Bug in :meth:`Series.median` and :meth:`DataFrame.median` with object-dtype values containing strings that can be converted to numbers (e.g. "2") returning incorrect numeric results; these now raise ``TypeError`` (:issue:`34671`)

pandas/core/frame.py

@@ -1620,15 +1620,18 @@ def dot(self, other: AnyArrayLike | DataFrame) -> DataFrame | Series:
                 )
 
         if isinstance(other, DataFrame):
+            common_type = find_common_type(list(self.dtypes) + list(other.dtypes))
             return self._constructor(
                 np.dot(lvals, rvals),
                 index=left.index,
                 columns=other.columns,
                 copy=False,
+                dtype=common_type,
             )
         elif isinstance(other, Series):
+            common_type = find_common_type(list(self.dtypes) + [other.dtypes])
             return self._constructor_sliced(
-                np.dot(lvals, rvals), index=left.index, copy=False
+                np.dot(lvals, rvals), index=left.index, copy=False, dtype=common_type
             )
         elif isinstance(rvals, (np.ndarray, Index)):
             result = np.dot(lvals, rvals)

pandas/tests/frame/methods/test_dot.py

@@ -129,3 +129,19 @@ def reduced_dim_assert(cls, result, expected):
         """
         tm.assert_series_equal(result, expected, check_names=False)
         assert result.name is None
+
+
+@pytest.mark.parametrize(
+    "dtype,exp_dtype",
+    [("Float32", "Float64"), ("Int16", "Int32"), ("float[pyarrow]", "double[pyarrow]")],
+)
+def test_arrow_dtype(dtype, exp_dtype):
+    pytest.importorskip("pyarrow")
+
+    cols = ["a", "b"]
+    df_a = DataFrame([[1, 2], [3, 4], [5, 6]], columns=cols, dtype="int32")
+    df_b = DataFrame([[1, 0], [0, 1]], index=cols, dtype=dtype)
+    result = df_a.dot(df_b)
+    expected = DataFrame([[1, 2], [3, 4], [5, 6]], dtype=exp_dtype)
+
+    tm.assert_frame_equal(result, expected)