diff --git a/sklearn/tests/test_docstrings.py b/sklearn/tests/test_docstrings.py
index 4271f862a2642..6e0b612b5bd9b 100644
--- a/sklearn/tests/test_docstrings.py
+++ b/sklearn/tests/test_docstrings.py
@@ -11,11 +11,6 @@
 
 numpydoc_validation = pytest.importorskip("numpydoc.validate")
 
-FUNCTION_DOCSTRING_IGNORE_LIST = [
-    "sklearn.utils.extmath.fast_logdet",
-]
-FUNCTION_DOCSTRING_IGNORE_LIST = set(FUNCTION_DOCSTRING_IGNORE_LIST)
-
 
 def get_all_methods():
     estimators = all_estimators()
@@ -142,11 +137,6 @@ def repr_errors(res, Klass=None, method: Optional[str] = None) -> str:
 @pytest.mark.parametrize("function_name", get_all_functions_names())
 def test_function_docstring(function_name, request):
     """Check function docstrings using numpydoc."""
-    if function_name in FUNCTION_DOCSTRING_IGNORE_LIST:
-        request.applymarker(
-            pytest.mark.xfail(run=False, reason="TODO pass numpydoc validation")
-        )
-
     res = numpydoc_validation.validate(function_name)
 
     res["errors"] = list(filter_errors(res["errors"], method="function"))
diff --git a/sklearn/utils/extmath.py b/sklearn/utils/extmath.py
index 35df3859324ae..675c51844e01f 100644
--- a/sklearn/utils/extmath.py
+++ b/sklearn/utils/extmath.py
@@ -82,15 +82,37 @@ def row_norms(X, squared=False):
 
 
 def fast_logdet(A):
-    """Compute log(det(A)) for A symmetric.
+    """Compute logarithm of determinant of a square matrix.
 
-    Equivalent to : np.log(nl.det(A)) but more robust.
-    It returns -Inf if det(A) is non positive or is not defined.
+    The (natural) logarithm of the determinant of a square matrix
+    is returned if det(A) is non-negative and well defined.
+    If the determinant is zero or negative returns -Inf.
+
+    Equivalent to : np.log(np.det(A)) but more robust.
 
     Parameters
     ----------
-    A : array-like
-        The matrix.
+    A : array_like of shape (n, n)
+        The square matrix.
+
+    Returns
+    -------
+    logdet : float
+        When det(A) is strictly positive, log(det(A)) is returned.
+        When det(A) is non-positive or not defined, then -inf is returned.
+
+    See Also
+    --------
+    numpy.linalg.slogdet : Compute the sign and (natural) logarithm of the determinant
+        of an array.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from sklearn.utils.extmath import fast_logdet
+    >>> a = np.array([[5, 1], [2, 8]])
+    >>> fast_logdet(a)
+    3.6375861597263857
     """
     sign, ld = np.linalg.slogdet(A)
     if not sign > 0: