class_docstr: Class for Lie groups.
  
  In this class, point_type ('vector' or 'matrix') will be used to describe
  the format of the points on the Lie group.
  If point_type is 'vector', the format of the inputs is
  [..., dimension], where dimension is the dimension of the Lie group.
  If point_type is 'matrix' the format of the inputs is
  [..., n, n] where n is the parameter of GL(n) e.g. the amount of rows
  and columns of the matrix.
  
  Parameters
  ----------
  dim : int
      Dimension of the Lie group.
  lie_algebra : MatrixLieAlgebra
      Lie algebra for matrix groups.
      Optional, default: None.
  
  Attributes
  ----------
  lie_algebra : MatrixLieAlgebra or None
      Tangent space at the identity.
docstr: Metric to equip the space with if equip is True.
docstr_tok: ["Metric","to","equip","the","space","with","if","equip","is","True","."]
code: def default_metric(self):
      """Metric to equip the space with if equip is True."""
      return (
          InvariantMetric,
          {"left": True, "metric_mat_at_identity": gs.eye(self.dim)},
      )
  
imports: import abc
  import geomstats.backend
  from geomstats.geometry.invariant_metric import InvariantMetric
  from geomstats.geometry.manifold import Manifold
  from geomstats.geometry.matrices import Matrices
label_desc: Use image node_id 2 for calling the LieGroup obj's underlying member method code with example usage: obj.default_metric() and returns: InvariantMetric,  dict