diff --git a/tests/unit/linalg/test_gramian.py b/tests/unit/linalg/test_gramian.py
index 4a02a9f4..6fc22512 100644
--- a/tests/unit/linalg/test_gramian.py
+++ b/tests/unit/linalg/test_gramian.py
@@ -1,6 +1,7 @@
 from pytest import mark
+from torch.testing import assert_close
 from utils.asserts import assert_is_psd_matrix
-from utils.tensors import randn_
+from utils.tensors import randn_, tensor_
 
 from torchjd._linalg import compute_gramian, is_matrix, normalize, regularize
 
@@ -25,6 +26,59 @@ def test_gramian_is_psd(shape: list[int]):
     assert_is_psd_matrix(gramian)
 
 
+def test_compute_gramian_scalar_input_0():
+    t = tensor_(5.0)
+    gramian = compute_gramian(t, contracted_dims=0)
+    expected = tensor_(25.0)
+
+    assert_close(gramian, expected)
+
+
+def test_compute_gramian_vector_input_0():
+    t = tensor_([2.0, 3.0])
+    gramian = compute_gramian(t, contracted_dims=0)
+    expected = tensor_([[4.0, 6.0], [6.0, 9.0]])
+
+    assert_close(gramian, expected)
+
+
+def test_compute_gramian_vector_input_1():
+    t = tensor_([2.0, 3.0])
+    gramian = compute_gramian(t, contracted_dims=1)
+    expected = tensor_(13.0)
+
+    assert_close(gramian, expected)
+
+
+def test_compute_gramian_matrix_input_0():
+    t = tensor_([[1.0, 2.0], [3.0, 4.0]])
+    gramian = compute_gramian(t, contracted_dims=0)
+    expected = tensor_(
+        [
+            [[[1.0, 3.0], [2.0, 4.0]], [[2.0, 6.0], [4.0, 8.0]]],
+            [[[3.0, 9.0], [6.0, 12.0]], [[4.0, 12.0], [8.0, 16.0]]],
+        ]
+    )
+
+    assert_close(gramian, expected)
+
+
+def test_compute_gramian_matrix_input_1():
+    t = tensor_([[1.0, 2.0], [3.0, 4.0]])
+    gramian = compute_gramian(t, contracted_dims=1)
+    expected = tensor_([[5.0, 11.0], [11.0, 25.0]])
+
+    assert_close(gramian, expected)
+
+
+def test_compute_gramian_matrix_input_2():
+    t = tensor_([[1.0, 2.0], [3.0, 4.0]])
+    gramian = compute_gramian(t, contracted_dims=2)
+    expected = tensor_(30.0)
+
+    assert_close(gramian, expected)
+
+
 @mark.parametrize(
     "shape",
     [