diff --git a/array_api_compat/common/_helpers.py b/array_api_compat/common/_helpers.py
index 60848b60..2467793c 100644
--- a/array_api_compat/common/_helpers.py
+++ b/array_api_compat/common/_helpers.py
@@ -276,7 +276,7 @@ def is_numpy_namespace(xp) -> bool:
     is_pydata_sparse_namespace
     is_array_api_strict_namespace
     """
-    return xp.__name__ in {'numpy', _compat_module_name + '.numpy'}
+    return xp.__name__ in {'numpy', _compat_module_name() + '.numpy'}
 
 def is_cupy_namespace(xp) -> bool:
     """
@@ -296,7 +296,7 @@ def is_cupy_namespace(xp) -> bool:
     is_pydata_sparse_namespace
     is_array_api_strict_namespace
     """
-    return xp.__name__ in {'cupy', _compat_module_name + '.cupy'}
+    return xp.__name__ in {'cupy', _compat_module_name() + '.cupy'}
 
 def is_torch_namespace(xp) -> bool:
     """
@@ -316,7 +316,7 @@ def is_torch_namespace(xp) -> bool:
     is_pydata_sparse_namespace
     is_array_api_strict_namespace
     """
-    return xp.__name__ in {'torch', _compat_module_name + '.torch'}
+    return xp.__name__ in {'torch', _compat_module_name() + '.torch'}
     
 
 def is_ndonnx_namespace(xp):
@@ -355,7 +355,7 @@ def is_dask_namespace(xp):
     is_pydata_sparse_namespace
     is_array_api_strict_namespace
     """
-    return xp.__name__ in {'dask.array', _compat_module_name + '.dask.array'}
+    return xp.__name__ in {'dask.array', _compat_module_name() + '.dask.array'}
 
 def is_jax_namespace(xp):
     """
diff --git a/tests/test_common.py b/tests/test_common.py
index 294a112a..e1cfa9eb 100644
--- a/tests/test_common.py
+++ b/tests/test_common.py
@@ -1,5 +1,9 @@
-from array_api_compat import (is_numpy_array, is_cupy_array, is_torch_array, # noqa: F401
-                              is_dask_array, is_jax_array, is_pydata_sparse_array)
+from array_api_compat import (  # noqa: F401
+    is_numpy_array, is_cupy_array, is_torch_array,
+    is_dask_array, is_jax_array, is_pydata_sparse_array,
+    is_numpy_namespace, is_cupy_namespace, is_torch_namespace,
+    is_dask_namespace, is_jax_namespace, is_pydata_sparse_namespace,
+)
 
 from array_api_compat import is_array_api_obj, device, to_device
 
@@ -10,7 +14,7 @@
 import array
 from numpy.testing import assert_allclose
 
-is_functions = {
+is_array_functions = {
     'numpy': 'is_numpy_array',
     'cupy': 'is_cupy_array',
     'torch': 'is_torch_array',
@@ -19,18 +23,38 @@
     'sparse': 'is_pydata_sparse_array',
 }
 
-@pytest.mark.parametrize('library', is_functions.keys())
-@pytest.mark.parametrize('func', is_functions.values())
+is_namespace_functions = {
+    'numpy': 'is_numpy_namespace',
+    'cupy': 'is_cupy_namespace',
+    'torch': 'is_torch_namespace',
+    'dask.array': 'is_dask_namespace',
+    'jax.numpy': 'is_jax_namespace',
+    'sparse': 'is_pydata_sparse_namespace',
+}
+
+
+@pytest.mark.parametrize('library', is_array_functions.keys())
+@pytest.mark.parametrize('func', is_array_functions.values())
 def test_is_xp_array(library, func):
     lib = import_(library)
     is_func = globals()[func]
 
     x = lib.asarray([1, 2, 3])
 
-    assert is_func(x) == (func == is_functions[library])
+    assert is_func(x) == (func == is_array_functions[library])
 
     assert is_array_api_obj(x)
 
+
+@pytest.mark.parametrize('library', is_namespace_functions.keys())
+@pytest.mark.parametrize('func', is_namespace_functions.values())
+def test_is_xp_namespace(library, func):
+    lib = import_(library)
+    is_func = globals()[func]
+
+    assert is_func(lib) == (func == is_namespace_functions[library])
+
+
 @pytest.mark.parametrize("library", all_libraries)
 def test_device(library):
     xp = import_(library, wrapper=True)
@@ -64,8 +88,8 @@ def test_to_device_host(library):
     assert_allclose(x, expected)
 
 
-@pytest.mark.parametrize("target_library", is_functions.keys())
-@pytest.mark.parametrize("source_library", is_functions.keys())
+@pytest.mark.parametrize("target_library", is_array_functions.keys())
+@pytest.mark.parametrize("source_library", is_array_functions.keys())
 def test_asarray_cross_library(source_library, target_library, request):
     if source_library == "dask.array" and target_library == "torch":
         # Allow rest of test to execute instead of immediately xfailing
@@ -81,7 +105,7 @@ def test_asarray_cross_library(source_library, target_library, request):
         pytest.skip(reason="`sparse` does not allow implicit densification")
     src_lib = import_(source_library, wrapper=True)
     tgt_lib = import_(target_library, wrapper=True)
-    is_tgt_type = globals()[is_functions[target_library]]
+    is_tgt_type = globals()[is_array_functions[target_library]]
 
     a = src_lib.asarray([1, 2, 3])
     b = tgt_lib.asarray(a)
@@ -96,7 +120,7 @@ def test_asarray_copy(library):
     # should be able to delete this.
     xp = import_(library, wrapper=True)
     asarray = xp.asarray
-    is_lib_func = globals()[is_functions[library]]
+    is_lib_func = globals()[is_array_functions[library]]
     all = xp.all if library != 'dask.array' else lambda x: xp.all(x).compute()
 
     if library == 'numpy' and xp.__version__[0] < '2' and not hasattr(xp, '_CopyMode') :
diff --git a/tests/test_vendoring.py b/tests/test_vendoring.py
index 66fc6984..70083b49 100644
--- a/tests/test_vendoring.py
+++ b/tests/test_vendoring.py
@@ -20,6 +20,7 @@ def test_vendoring_torch():
 
     uses_torch._test_torch()
 
+
 def test_vendoring_dask():
     from vendor_test import uses_dask
     uses_dask._test_dask()
diff --git a/vendor_test/uses_cupy.py b/vendor_test/uses_cupy.py
index 97f710b9..e3bbdebe 100644
--- a/vendor_test/uses_cupy.py
+++ b/vendor_test/uses_cupy.py
@@ -1,6 +1,10 @@
 # Basic test that vendoring works
 
-from .vendored._compat import cupy as cp_compat
+from .vendored._compat import (
+    cupy as cp_compat,
+    is_cupy_array,
+    is_cupy_namespace,
+)
 
 import cupy as cp
 
@@ -16,3 +20,6 @@ def _test_cupy():
     assert isinstance(res, cp.ndarray)
 
     cp.testing.assert_allclose(res, [1., 2., 9.])
+
+    assert is_cupy_array(res)
+    assert is_cupy_namespace(cp) and is_cupy_namespace(cp_compat)
diff --git a/vendor_test/uses_dask.py b/vendor_test/uses_dask.py
index 65a00916..44fa8f2f 100644
--- a/vendor_test/uses_dask.py
+++ b/vendor_test/uses_dask.py
@@ -1,6 +1,7 @@
 # Basic test that vendoring works
 
 from .vendored._compat.dask import array as dask_compat
+from .vendored._compat import is_dask_array, is_dask_namespace
 
 import dask.array as da
 import numpy as np
@@ -17,3 +18,6 @@ def _test_dask():
     assert isinstance(res, da.Array)
 
     np.testing.assert_allclose(res, [1., 2., 9.])
+
+    assert is_dask_array(res)
+    assert is_dask_namespace(da) and is_dask_namespace(dask_compat)
diff --git a/vendor_test/uses_numpy.py b/vendor_test/uses_numpy.py
index 96f2c5ff..d7a68248 100644
--- a/vendor_test/uses_numpy.py
+++ b/vendor_test/uses_numpy.py
@@ -1,6 +1,11 @@
 # Basic test that vendoring works
 
-from .vendored._compat import numpy as np_compat
+from .vendored._compat import (
+    is_numpy_array,
+    is_numpy_namespace,
+    numpy as np_compat,
+)
+
 
 import numpy as np
 
@@ -16,3 +21,6 @@ def _test_numpy():
     assert isinstance(res, np.ndarray)
 
     np.testing.assert_allclose(res, [1., 2., 9.])
+
+    assert is_numpy_array(res)
+    assert is_numpy_namespace(np) and is_numpy_namespace(np_compat)
diff --git a/vendor_test/uses_torch.py b/vendor_test/uses_torch.py
index b828ad33..5804aaff 100644
--- a/vendor_test/uses_torch.py
+++ b/vendor_test/uses_torch.py
@@ -1,6 +1,10 @@
 # Basic test that vendoring works
 
-from .vendored._compat import torch as torch_compat
+from .vendored._compat import (
+    is_torch_array,
+    is_torch_namespace,
+    torch as torch_compat,
+)
 
 import torch
 
@@ -20,3 +24,7 @@ def _test_torch():
     assert isinstance(res, torch.Tensor)
 
     torch.testing.assert_allclose(res, [[1., 2., 3.]])
+
+    assert is_torch_array(res)
+    assert is_torch_namespace(torch) and is_torch_namespace(torch_compat)
+