diff --git a/tests/test_utils.py b/tests/test_utils.py
index b584530..229d9da 100644
--- a/tests/test_utils.py
+++ b/tests/test_utils.py
@@ -7,17 +7,20 @@
 def test_proj():
     rng = np.random.RandomState(0)
     X = rng.normal(0, 1, (100, 2))
-    Z = rng.normal(0, 1, (100, 5))
+    Z = rng.normal(0, 1, (100, 4)) @ rng.normal(0, 1, (4, 6))
 
-    assert np.allclose(proj(Z, X), Z @ np.linalg.inv(Z.T @ Z) @ Z.T @ X)
+    assert np.allclose(proj(Z, X), Z @ np.linalg.pinv(Z.T @ Z) @ Z.T @ X)
+    assert np.allclose(proj(Z, X), proj(Z, proj(Z, X)))
+    assert np.allclose(proj(proj(Z, X), X), proj(Z, X))
 
 
 def test_oproj():
     rng = np.random.RandomState(0)
     X = rng.normal(0, 1, (100, 2))
-    Z = rng.normal(0, 1, (100, 5))
+    Z = rng.normal(0, 1, (100, 4)) @ rng.normal(0, 1, (4, 6))
 
     assert np.allclose(X - proj(Z, X), oproj(Z, X))
+    assert np.allclose(oproj(Z, X), oproj(Z, oproj(Z, X)))
 
 
 def test_proj_multiple_args():