diff --git a/docs/jax.numpy.rst b/docs/jax.numpy.rst
index d4cfd63c0f0a..12e795ecf582 100644
--- a/docs/jax.numpy.rst
+++ b/docs/jax.numpy.rst
@@ -449,6 +449,7 @@ jax.numpy.linalg
 
   cholesky
   cond
+  cross
   det
   eig
   eigh
@@ -460,6 +461,7 @@ jax.numpy.linalg
   matrix_rank
   multi_dot
   norm
+  outer
   pinv
   qr
   slogdet
diff --git a/jax/_src/numpy/linalg.py b/jax/_src/numpy/linalg.py
index 0934e97d35cc..3a8410acf384 100644
--- a/jax/_src/numpy/linalg.py
+++ b/jax/_src/numpy/linalg.py
@@ -677,3 +677,24 @@ def lstsq(a: ArrayLike, b: ArrayLike, rcond: Optional[float] = None, *,
   if numpy_resid:
     return _lstsq(a, b, rcond, numpy_resid=True)
   return _jit_lstsq(a, b, rcond)
+
+
+@_wraps(getattr(np.linalg, "cross", None))
+def cross(x1: ArrayLike, x2: ArrayLike, /, *, axis=-1):
+  check_arraylike("jnp.linalg.outer", x1, x2)
+  x1, x2 = jnp.asarray(x1), jnp.asarray(x2)
+  if x1.shape[axis] != 3 or x2.shape[axis] != 3:
+    raise ValueError(
+        "Both input arrays must be (arrays of) 3-dimensional vectors, "
+        f"but they have {x1.shape[axis]=} and {x2.shape[axis]=}"
+    )
+  return jnp.cross(x1, x2, axis=axis)
+
+
+@_wraps(getattr(np.linalg, "outer", None))
+def outer(x1: ArrayLike, x2: ArrayLike, /) -> Array:
+  check_arraylike("jnp.linalg.outer", x1, x2)
+  x1, x2 = jnp.asarray(x1), jnp.asarray(x2)
+  if x1.ndim != 1 or x2.ndim != 1:
+    raise ValueError(f"Input arrays must be one-dimensional, but they are {x1.ndim=} {x2.ndim=}")
+  return x1[:, None] * x2[None, :]
diff --git a/jax/experimental/array_api/_linear_algebra_functions.py b/jax/experimental/array_api/_linear_algebra_functions.py
index 2ce616afd3b7..154d963a765d 100644
--- a/jax/experimental/array_api/_linear_algebra_functions.py
+++ b/jax/experimental/array_api/_linear_algebra_functions.py
@@ -47,7 +47,7 @@ def cross(x1, x2, /, *, axis=-1):
   """
   Returns the cross product of 3-element vectors.
   """
-  return jax.numpy.cross(x1, x2, axis=axis)
+  return jax.numpy.linalg.cross(x1, x2, axis=axis)
 
 def det(x, /):
   """
@@ -115,7 +115,7 @@ def outer(x1, x2, /):
   """
   Returns the outer product of two vectors x1 and x2.
   """
-  return jax.numpy.outer(x1, x2)
+  return jax.numpy.linalg.outer(x1, x2)
 
 def pinv(x, /, *, rtol=None):
   """
diff --git a/jax/numpy/linalg.py b/jax/numpy/linalg.py
index 88f9b3781603..42536822ce5a 100644
--- a/jax/numpy/linalg.py
+++ b/jax/numpy/linalg.py
@@ -17,6 +17,7 @@
 
 from jax._src.numpy.linalg import (
   cholesky as cholesky,
+  cross as cross,
   det as det,
   eig as eig,
   eigh as eigh,
@@ -27,6 +28,7 @@
   matrix_power as matrix_power,
   matrix_rank as matrix_rank,
   norm as norm,
+  outer as outer,
   pinv as pinv,
   qr as qr,
   slogdet as slogdet,
diff --git a/tests/linalg_test.py b/tests/linalg_test.py
index c4295d53535c..1f73471a307a 100644
--- a/tests/linalg_test.py
+++ b/tests/linalg_test.py
@@ -1092,6 +1092,45 @@ def f(inp):
     cube_func = jax.jacfwd(hess_func)
     self.assertFalse(np.any(np.isnan(cube_func(a))))
 
+  @jtu.sample_product(
+    [dict(lhs_shape=lhs_shape, rhs_shape=rhs_shape, axis=axis)
+      for lhs_shape, rhs_shape, axis in [
+          [(3,), (3,), -1],
+          [(2, 3), (2, 3), -1],
+          [(3, 4), (3, 4), 0],
+          [(3, 5), (3, 4, 5), 0]
+      ]],
+    lhs_dtype=jtu.dtypes.numeric,
+    rhs_dtype=jtu.dtypes.numeric,
+  )
+  @jax.numpy_rank_promotion('allow')  # This test explicitly exercises implicit rank promotion.
+  def testCross(self, lhs_shape, rhs_shape, lhs_dtype, rhs_dtype, axis):
+    rng = jtu.rand_default(self.rng())
+    args_maker = lambda: [rng(lhs_shape, lhs_dtype), rng(rhs_shape, rhs_dtype)]
+    lax_fun = partial(jnp.linalg.cross, axis=axis)
+    np_fun = jtu.promote_like_jnp(partial(
+      np.cross if jtu.numpy_version() < (2, 0, 0) else np.linalg.cross,
+      axis=axis))
+    with jtu.strict_promotion_if_dtypes_match([lhs_dtype, rhs_dtype]):
+      self._CheckAgainstNumpy(np_fun, lax_fun, args_maker)
+      self._CompileAndCheck(lax_fun, args_maker)
+
+  @jtu.sample_product(
+      lhs_shape=[(0,), (3,), (5,)],
+      rhs_shape=[(0,), (3,), (5,)],
+      lhs_dtype=jtu.dtypes.numeric,
+      rhs_dtype=jtu.dtypes.numeric,
+  )
+  def testOuter(self, lhs_shape, rhs_shape, lhs_dtype, rhs_dtype):
+    rng = jtu.rand_default(self.rng())
+    args_maker = lambda: [rng(lhs_shape, lhs_dtype), rng(rhs_shape, rhs_dtype)]
+    lax_fun = jnp.linalg.outer
+    np_fun = jtu.promote_like_jnp(
+      np.outer if jtu.numpy_version() < (2, 0, 0) else np.linalg.outer)
+    with jtu.strict_promotion_if_dtypes_match([lhs_dtype, rhs_dtype]):
+      self._CheckAgainstNumpy(np_fun, lax_fun, args_maker)
+      self._CompileAndCheck(lax_fun, args_maker)
+
 
 class ScipyLinalgTest(jtu.JaxTestCase):