class_docstr: Base class to represent the So3 group.
  
  The SO(3) is the group of all rotations about the origin of three-dimensional Euclidean space
  :math:`R^3` under the operation of composition.
  See more: https://en.wikipedia.org/wiki/3D_rotation_group
  
  We internally represent the rotation by a unit quaternion.
  
  Example:
      >>> q = Quaternion.identity()
      >>> s = So3(q)
      >>> s.q
      Parameter containing:
      tensor([1., 0., 0., 0.], requires_grad=True)
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docstr: Converts elements from lie algebra to vector space. Returns vector of shape :math:`(B,3)`.
  
  .. math::
      omega = \begin{bmatrix} 0 & -c & b \\
      c & 0 & -a \\
      -b & a & 0\end{bmatrix}
  
  Args:
      omega: 3x3-matrix representing lie algebra.
  
  Example:
      >>> v = torch.ones((1,3))
      >>> omega = So3.hat(v)
      >>> So3.vee(omega)
      tensor([[1., 1., 1.]])
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code: def vee(omega: Tensor) -> Tensor:
      r"""Converts elements from lie algebra to vector space. Returns vector of shape :math:`(B,3)`.
  
          .. math::
              omega = \begin{bmatrix} 0 & -c & b \\
              c & 0 & -a \\
              -b & a & 0\end{bmatrix}
  
          Args:
              omega: 3x3-matrix representing lie algebra.
  
          Example:
              >>> v = torch.ones((1,3))
              >>> omega = So3.hat(v)
              >>> So3.vee(omega)
              tensor([[1., 1., 1.]])
          """
      # KORNIA_CHECK_SHAPE(omega, ["B", "3", "3"])  # FIXME: resolve shape bugs. @edgarriba
      a, b, c = omega[..., 2, 1], omega[..., 0, 2], omega[..., 1, 0]
      return stack((a, b, c), -1)
  
imports: from __future__ import annotations
  from typing import Optional
  from kornia.core import Device, Dtype, Module, Tensor, concatenate, eye, stack, tensor, where, zeros, zeros_like
  from kornia.core.check import KORNIA_CHECK_TYPE
  from kornia.geometry.conversions import vector_to_skew_symmetric_matrix
  from kornia.geometry.linalg import batched_dot_product
  from kornia.geometry.quaternion import Quaternion
  from kornia.geometry.vector import Vector3
label_desc: Use image node_id 9 for calling the So3 obj's underlying member method code with example usage: obj.vee(omega) and returns: stack