diff --git a/docs/jax.numpy.rst b/docs/jax.numpy.rst
index 12e795ecf582..1de86ca84c19 100644
--- a/docs/jax.numpy.rst
+++ b/docs/jax.numpy.rst
@@ -457,8 +457,10 @@ jax.numpy.linalg
   eigvalsh
   inv
   lstsq
+  matrix_norm
   matrix_power
   matrix_rank
+  matrix_transpose
   multi_dot
   norm
   outer
@@ -469,6 +471,8 @@ jax.numpy.linalg
   svd
   tensorinv
   tensorsolve
+  vector_norm
+  vecdot
 
 JAX Array
 ---------
diff --git a/jax/_src/numpy/linalg.py b/jax/_src/numpy/linalg.py
index 4e4d114f1543..850ffb8377b1 100644
--- a/jax/_src/numpy/linalg.py
+++ b/jax/_src/numpy/linalg.py
@@ -699,3 +699,52 @@ def outer(x1: ArrayLike, x2: ArrayLike, /) -> Array:
   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, :]
+
+
+@_wraps(getattr(np.linalg, "matrix_norm", None))
+def matrix_norm(x: ArrayLike, /, *, keepdims: bool = False, ord: str = 'fro') -> Array:
+  """
+  Computes the matrix norm of a matrix (or a stack of matrices) x.
+  """
+  check_arraylike('jnp.linalg.matrix_norm', x)
+  return norm(x, ord=ord, keepdims=keepdims, axis=(-2, -1))
+
+
+@_wraps(getattr(np.linalg, "matrix_transpose", None))
+def matrix_transpose(x: ArrayLike, /) -> Array:
+  """Transposes a matrix (or a stack of matrices) x."""
+  check_arraylike('jnp.linalg.matrix_transpose', x)
+  x_arr = jnp.asarray(x)
+  ndim = x_arr.ndim
+  if ndim < 2:
+    raise ValueError(f"matrix_transpose requres at least 2 dimensions; got {ndim=}")
+  return jax.lax.transpose(x_arr, (*range(ndim - 2), ndim - 1, ndim - 2))
+
+
+@_wraps(getattr(np.linalg, "vector_norm", None))
+def vector_norm(x: ArrayLike, /, *, axis: int | None = None, keepdims: bool = False,
+                ord: int | str = 2) -> Array:
+  """Computes the vector norm of a vector (or batch of vectors) x."""
+  check_arraylike('jnp.linalg.vector_norm', x)
+  if axis is None:
+    result = norm(jnp.ravel(x), ord=ord)
+    if keepdims:
+      result = lax.expand_dims(result, range(jnp.ndim(x)))
+    return result
+  return norm(x, axis=axis, keepdims=keepdims, ord=ord)
+
+
+@_wraps(getattr(np.linalg, "vecdot", None))
+def vecdot(x1: ArrayLike, x2: ArrayLike, /, *, axis: int = -1) -> Array:
+  """Computes the (vector) dot product of two arrays."""
+  check_arraylike("jnp.linalg.vecdot", x1, x2)
+  x1_arr, x2_arr = jnp.asarray(x1), jnp.asarray(x2)
+  rank = max(x1_arr.ndim, x2_arr.ndim)
+  x1_arr = jax.lax.broadcast_to_rank(x1_arr, rank)
+  x2_arr = jax.lax.broadcast_to_rank(x2_arr, rank)
+  if x1_arr.shape[axis] != x2_arr.shape[axis]:
+    raise ValueError("x1 and x2 must have the same size along specified axis.")
+  x1_arr = jax.numpy.moveaxis(x1_arr, axis, -1)
+  x2_arr = jax.numpy.moveaxis(x2_arr, axis, -1)
+  # TODO(jakevdp): call lax.dot_general directly
+  return jax.numpy.matmul(x1_arr[..., None, :], x2_arr[..., None])[..., 0, 0]
diff --git a/jax/experimental/array_api/_linear_algebra_functions.py b/jax/experimental/array_api/_linear_algebra_functions.py
index 154d963a765d..1a144773f44a 100644
--- a/jax/experimental/array_api/_linear_algebra_functions.py
+++ b/jax/experimental/array_api/_linear_algebra_functions.py
@@ -91,7 +91,7 @@ def matrix_norm(x, /, *, keepdims=False, ord='fro'):
   """
   Computes the matrix norm of a matrix (or a stack of matrices) x.
   """
-  return jax.numpy.linalg.norm(x, ord=ord, keepdims=keepdims, axis=(-1, -2))
+  return jax.numpy.linalg.matrix_norm(x, ord=ord, keepdims=keepdims)
 
 def matrix_power(x, n, /):
   """
@@ -107,9 +107,7 @@ def matrix_rank(x, /, *, rtol=None):
 
 def matrix_transpose(x, /):
   """Transposes a matrix (or a stack of matrices) x."""
-  if x.ndim < 2:
-    raise ValueError(f"matrix_transpose requres at least 2 dimensions; got {x.ndim=}")
-  return jax.lax.transpose(x, (*range(x.ndim - 2), x.ndim - 1, x.ndim - 2))
+  return jax.numpy.linalg.matrix_transpose(x)
 
 def outer(x1, x2, /):
   """
@@ -177,16 +175,8 @@ def trace(x, /, *, offset=0, dtype=None):
 
 def vecdot(x1, x2, /, *, axis=-1):
   """Computes the (vector) dot product of two arrays."""
-  rank = max(x1.ndim, x2.ndim)
-  x1 = jax.lax.broadcast_to_rank(x1, rank)
-  x2 = jax.lax.broadcast_to_rank(x2, rank)
-  if x1.shape[axis] != x2.shape[axis]:
-    raise ValueError("x1 and x2 must have the same size along specified axis.")
-  x1, x2 = jax.numpy.broadcast_arrays(x1, x2)
-  x1 = jax.numpy.moveaxis(x1, axis, -1)
-  x2 = jax.numpy.moveaxis(x2, axis, -1)
-  return jax.numpy.matmul(x1[..., None, :], x2[..., None])[..., 0, 0]
+  return jax.numpy.linalg.vecdot(x1, x2, axis=axis)
 
 def vector_norm(x, /, *, axis=None, keepdims=False, ord=2):
   """Computes the vector norm of a vector (or batch of vectors) x."""
-  return jax.numpy.linalg.norm(x, axis=axis, keepdims=keepdims, ord=ord)
+  return jax.numpy.linalg.vector_norm(x, axis=axis, keepdims=keepdims, ord=ord)
diff --git a/jax/experimental/array_api/linalg.py b/jax/experimental/array_api/linalg.py
index 30b531f502bc..49c93c5b1908 100644
--- a/jax/experimental/array_api/linalg.py
+++ b/jax/experimental/array_api/linalg.py
@@ -20,7 +20,6 @@
   eigh as eigh,
   eigvalsh as eigvalsh,
   inv as inv,
-  jax as jax,
   matmul as matmul,
   matrix_norm as matrix_norm,
   matrix_power as matrix_power,
diff --git a/jax/numpy/linalg.py b/jax/numpy/linalg.py
index 42536822ce5a..a5ee94c8a075 100644
--- a/jax/numpy/linalg.py
+++ b/jax/numpy/linalg.py
@@ -25,8 +25,10 @@
   eigvalsh as eigvalsh,
   inv as inv,
   lstsq as lstsq,
+  matrix_norm as matrix_norm,
   matrix_power as matrix_power,
   matrix_rank as matrix_rank,
+  matrix_transpose as matrix_transpose,
   norm as norm,
   outer as outer,
   pinv as pinv,
@@ -34,6 +36,8 @@
   slogdet as slogdet,
   solve as solve,
   svd as svd,
+  vector_norm as vector_norm,
+  vecdot as vecdot,
 )
 from jax._src.third_party.numpy.linalg import (
   cond as cond,
diff --git a/tests/array_api_test.py b/tests/array_api_test.py
index 97fc682398e4..0d4893e4939e 100644
--- a/tests/array_api_test.py
+++ b/tests/array_api_test.py
@@ -175,7 +175,6 @@
   'eigh',
   'eigvalsh',
   'inv',
-  'jax',
   'matmul',
   'matrix_norm',
   'matrix_power',
diff --git a/tests/linalg_test.py b/tests/linalg_test.py
index 1f73471a307a..948349cfe035 100644
--- a/tests/linalg_test.py
+++ b/tests/linalg_test.py
@@ -612,6 +612,70 @@ def testStringInfNorm(self):
     with self.assertRaisesRegex(err, msg):
       jnp.linalg.norm(jnp.array([1.0, 2.0, 3.0]), ord="inf")
 
+  @jtu.sample_product(
+      shape=[(2, 3), (4, 2, 3), (2, 3, 4, 5)],
+      dtype=float_types + complex_types,
+      keepdims=[True, False],
+      ord=[1, -1, 2, -2, np.inf, -np.inf, 'fro', 'nuc'],
+  )
+  def testMatrixNorm(self, shape, dtype, keepdims, ord):
+    rng = jtu.rand_default(self.rng())
+    args_maker = lambda: [rng(shape, dtype)]
+    if jtu.numpy_version() < (2, 0, 0):
+      np_fn = partial(np.linalg.norm, ord=ord, keepdims=keepdims, axis=(-2, -1))
+    else:
+      np_fn = partial(np.linalg.matrix_norm, ord=ord, keepdims=keepdims)
+    np_fn = jtu.promote_like_jnp(np_fn, inexact=True)
+    jnp_fn = partial(jnp.linalg.matrix_norm, ord=ord, keepdims=keepdims)
+    self._CheckAgainstNumpy(np_fn, jnp_fn, args_maker, tol=1e-3)
+    self._CompileAndCheck(jnp_fn, args_maker)
+
+  @jtu.sample_product(
+      shape=[(3,), (3, 4), (2, 3, 4, 5)],
+      dtype=float_types + complex_types,
+      keepdims=[True, False],
+      axis=[0, None],
+      ord=[1, -1, 2, -2, np.inf, -np.inf],
+  )
+  def testVectorNorm(self, shape, dtype, keepdims, axis, ord):
+    rng = jtu.rand_default(self.rng())
+    args_maker = lambda: [rng(shape, dtype)]
+    if jtu.numpy_version() < (2, 0, 0):
+      def np_fn(x, ord=ord, keepdims=keepdims, axis=axis):
+        if axis is None:
+          result = np_fn(x.ravel(), ord, keepdims=False, axis=0)
+          return np.reshape(result, (1,) * x.ndim) if keepdims else result
+        return np.linalg.norm(x, ord=ord, keepdims=keepdims, axis=axis)
+    else:
+      np_fn = partial(np.linalg.vector_norm, ord=ord, keepdims=keepdims, axis=axis)
+    np_fn = jtu.promote_like_jnp(np_fn, inexact=True)
+    jnp_fn = partial(jnp.linalg.vector_norm, ord=ord, keepdims=keepdims, axis=axis)
+    self._CheckAgainstNumpy(np_fn, jnp_fn, args_maker, tol=1e-3)
+    self._CompileAndCheck(jnp_fn, args_maker)
+
+  @jtu.sample_product(
+      [dict(lhs_shape=(2, 3, 4), rhs_shape=(1, 4), axis=-1),
+       dict(lhs_shape=(2, 3, 4), rhs_shape=(2, 1, 1), axis=0),
+       dict(lhs_shape=(2, 3, 4), rhs_shape=(3, 4), axis=1)],
+      dtype=float_types + complex_types,
+  )
+  def testVecDot(self, lhs_shape, rhs_shape, axis, dtype):
+    rng = jtu.rand_default(self.rng())
+    args_maker = lambda: [rng(lhs_shape, dtype), rng(rhs_shape, dtype)]
+    if jtu.numpy_version() < (2, 0, 0):
+      def np_fn(x, y, axis=axis):
+        x, y = np.broadcast_arrays(x, y)
+        x = np.moveaxis(x, axis, -1)
+        y = np.moveaxis(y, axis, -1)
+        return np.matmul(x[..., None, :], y[..., None])[..., 0, 0]
+    else:
+      np_fn = partial(np.linalg.vecdot, axis=axis)
+    np_fn = jtu.promote_like_jnp(np_fn, inexact=True)
+    jnp_fn = partial(jnp.linalg.vecdot, axis=axis)
+    self._CheckAgainstNumpy(np_fn, jnp_fn, args_maker, tol=1e-3)
+    self._CompileAndCheck(jnp_fn, args_maker)
+
+
   @jtu.sample_product(
       [
           dict(m=m, n=n, full_matrices=full_matrices, hermitian=hermitian)
@@ -1905,6 +1969,21 @@ def testSchurBatching(self, shape, dtype):
     Ts, Ss = vmap(lax.linalg.schur)(args)
     self.assertAllClose(reconstruct(Ss, Ts), args, atol=1e-4)
 
+  @jtu.sample_product(
+    shape=[(2, 3), (2, 3, 4), (2, 3, 4, 5)],
+    dtype=float_types + complex_types,
+  )
+  def testMatrixTranspose(self, shape, dtype):
+    rng = jtu.rand_default(self.rng())
+    args_maker = lambda: [rng(shape, dtype)]
+    jnp_fun = jnp.linalg.matrix_transpose
+    if jtu.numpy_version() < (2, 0, 0):
+      np_fun = lambda x: np.swapaxes(x, -1, -2)
+    else:
+      np_fun = np.linalg.matrix_transpose
+    self._CheckAgainstNumpy(np_fun, jnp_fun, args_maker)
+    self._CompileAndCheck(jnp_fun, args_maker)
+
 
 if __name__ == "__main__":
   absltest.main(testLoader=jtu.JaxTestLoader())