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BUG: np.linalg.svd(..., hermitian=True) returns non-unitary vh (#31347) #31459

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Merged
charris merged 1 commit into from
May 18, 2026
+8 −2
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BUG: np.linalg.svd(..., hermitian=True) returns non-unitary vh (#31347) #31459

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

* Explicitly remove 0 from eigenvalue signs to ensure that vh is unitary.
* Add Hermitian SVD test that has 0 as a singular value.
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@EarlMilktea @charris
EarlMilktea authored and charris committed May 18, 2026
commit d1bffeb9ec4ec0bf029c94ea35abffa92d5c30f2
4 changes: 2 additions & 2 deletions numpy/linalg/_linalg.py
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Original file line number Diff line number Diff line change
Expand Up @@ -61,7 +61,6 @@
overrides,
prod,
reciprocal,
sign,
single,
sort,
sqrt,
Expand Down Expand Up @@ -1810,7 +1809,8 @@ 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)
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6 changes: 6 additions & 0 deletions numpy/linalg/tests/test_linalg.py
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Expand Up @@ -745,6 +745,12 @@ 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)
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