BUG: np.linalg.svd(..., hermitian=True) returns non-unitary vh (#31347)

EarlMilktea · web-flow · commit bba3954559e6 · 2026-05-18T10:07:50.000-04:00
* Explicitly remove 0 from eigenvalue signs to ensure that vh is unitary.
* Add Hermitian SVD test that has 0 as a singular value.
diff --git a/numpy/linalg/_linalg.py b/numpy/linalg/_linalg.py
@@ -61,7 +61,6 @@
     overrides,
     prod,
     reciprocal,
-    sign,
     single,
     sort,
     sqrt,
@@ -1809,7 +1808,8 @@ def svd(a, full_matrices=True, compute_uv=True, hermitian=False):
         # and related arrays to have the correct order
         if compute_uv:
             s, u = eigh(a)
-            sgn = sign(s)
+            # avoid zero sign
+            sgn = np.copysign(1.0, s)
             s = abs(s)
             sidx = argsort(s)[..., ::-1]
             sgn = np.take_along_axis(sgn, sidx, axis=-1)
diff --git a/numpy/linalg/tests/test_linalg.py b/numpy/linalg/tests/test_linalg.py
@@ -765,6 +765,12 @@ def hermitian(mat):
 class TestSVDHermitian(SVDHermitianCases, SVDBaseTests):
     hermitian = True
 
+    def test_singular(self):
+        x = np.array([[1, 0], [0, 0]])
+        u, _, vh = linalg.svd(x, hermitian=self.hermitian)
+        assert_allclose(u @ u.T.conj(), np.eye(2), rtol=1e-14)
+        assert_allclose(vh @ vh.T.conj(), np.eye(2), rtol=1e-14)
+
 
 class CondCases(LinalgSquareTestCase, LinalgGeneralizedSquareTestCase):
     # cond(x, p) for p in (None, 2, -2)
