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+from __future__ import annotations
+
+import torch
+from typing import Optional, Union, Tuple
+
+from torch.linalg import * # noqa: F403
+
+# torch.linalg doesn't define __all__
+# from torch.linalg import __all__ as linalg_all
+from torch import linalg as torch_linalg
+linalg_all = [i for i in dir(torch_linalg) if not i.startswith('_')]
+
+# outer is implemented in torch but aren't in the linalg namespace
+from torch import outer
+from ._aliases import _fix_promotion, sum
+# These functions are in both the main and linalg namespaces
+from ._aliases import matmul, matrix_transpose, tensordot
+from ._typing import Array, DType
+from ..common._typing import JustInt, JustFloat
+
+# Note: torch.linalg.cross does not default to axis=-1 (it defaults to the
+# first axis with size 3), see https://github.com/pytorch/pytorch/issues/58743
+
+# torch.cross also does not support broadcasting when it would add new
+# dimensions https://github.com/pytorch/pytorch/issues/39656
+def cross(x1: Array, x2: Array, /, *, axis: int = -1) -> Array:
+    x1, x2 = _fix_promotion(x1, x2, only_scalar=False)
+    if not (-min(x1.ndim, x2.ndim) <= axis < max(x1.ndim, x2.ndim)):
+        raise ValueError(f"axis {axis} out of bounds for cross product of arrays with shapes {x1.shape} and {x2.shape}")
+    if not (x1.shape[axis] == x2.shape[axis] == 3):
+        raise ValueError(f"cross product axis must have size 3, got {x1.shape[axis]} and {x2.shape[axis]}")
+    x1, x2 = torch.broadcast_tensors(x1, x2)
+    return torch_linalg.cross(x1, x2, dim=axis)
+
+def vecdot(x1: Array, x2: Array, /, *, axis: int = -1, **kwargs) -> Array:
+    from ._aliases import isdtype
+
+    x1, x2 = _fix_promotion(x1, x2, only_scalar=False)
+
+    # torch.linalg.vecdot incorrectly allows broadcasting along the contracted dimension
+    if x1.shape[axis] != x2.shape[axis]:
+        raise ValueError("x1 and x2 must have the same size along the given axis")
+
+    # torch.linalg.vecdot doesn't support integer dtypes
+    if isdtype(x1.dtype, 'integral') or isdtype(x2.dtype, 'integral'):
+        if kwargs:
+            raise RuntimeError("vecdot kwargs not supported for integral dtypes")
+
+        x1_ = torch.moveaxis(x1, axis, -1)
+        x2_ = torch.moveaxis(x2, axis, -1)
+        x1_, x2_ = torch.broadcast_tensors(x1_, x2_)
+
+        res = x1_[..., None, :] @ x2_[..., None]
+        return res[..., 0, 0]
+    return torch.linalg.vecdot(x1, x2, dim=axis, **kwargs)
+
+def solve(x1: Array, x2: Array, /, **kwargs) -> Array:
+    x1, x2 = _fix_promotion(x1, x2, only_scalar=False)
+    # Torch tries to emulate NumPy 1 solve behavior by using batched 1-D solve
+    # whenever
+    # 1. x1.ndim - 1 == x2.ndim
+    # 2. x1.shape[:-1] == x2.shape
+    #
+    # See linalg_solve_is_vector_rhs in
+    # aten/src/ATen/native/LinearAlgebraUtils.h and
+    # TORCH_META_FUNC(_linalg_solve_ex) in
+    # aten/src/ATen/native/BatchLinearAlgebra.cpp in the PyTorch source code.
+    #
+    # The easiest way to work around this is to prepend a size 1 dimension to
+    # x2, since x2 is already one dimension less than x1.
+    #
+    # See https://github.com/pytorch/pytorch/issues/52915
+    if x2.ndim != 1 and x1.ndim - 1 == x2.ndim and x1.shape[:-1] == x2.shape:
+        x2 = x2[None]
+    return torch.linalg.solve(x1, x2, **kwargs)
+
+# torch.trace doesn't support the offset argument and doesn't support stacking
+def trace(x: Array, /, *, offset: int = 0, dtype: Optional[DType] = None) -> Array:
+    # Use our wrapped sum to make sure it does upcasting correctly
+    return sum(torch.diagonal(x, offset=offset, dim1=-2, dim2=-1), axis=-1, dtype=dtype)
+
+def vector_norm(
+    x: Array,
+    /,
+    *,
+    axis: Optional[Union[int, Tuple[int, ...]]] = None,
+    keepdims: bool = False,
+    # JustFloat stands for inf | -inf, which are not valid for Literal
+    ord: JustInt | JustFloat = 2,
+    **kwargs,
+) -> Array:
+    # torch.vector_norm incorrectly treats axis=() the same as axis=None
+    if axis == ():
+        out = kwargs.get('out')
+        if out is None:
+            dtype = None
+            if x.dtype == torch.complex64:
+                dtype = torch.float32
+            elif x.dtype == torch.complex128:
+                dtype = torch.float64
+
+            out = torch.zeros_like(x, dtype=dtype)
+
+        # The norm of a single scalar works out to abs(x) in every case except
+        # for ord=0, which is x != 0.
+        if ord == 0:
+            out[:] = (x != 0)
+        else:
+            out[:] = torch.abs(x)
+        return out
+    return torch.linalg.vector_norm(x, ord=ord, axis=axis, keepdim=keepdims, **kwargs)
+
+__all__ = linalg_all + ['outer', 'matmul', 'matrix_transpose', 'tensordot',
+                        'cross', 'vecdot', 'solve', 'trace', 'vector_norm']
+
+_all_ignore = ['torch_linalg', 'sum']
+
+del linalg_all
+
+def __dir__() -> list[str]:
+    return __all__