class_docstr: Class for invariant metrics on Lie groups represented by vectors.
  
  Parameters
  ----------
  space : LieGroup
      Group to equip with the invariant metric
  left : bool
      Whether to use a left or right invariant metric.
      Optional, default: True.
class_docstr_tok: ["Class","for","invariant","metrics","on","Lie","groups","represented","by","vectors",".","Parameters","--","--","--","--","--","space",":","LieGroup","Group","to","equip","with","the","invariant","metric","left",":","bool","Whether","to","use","a","left","or","right","invariant","metric",".","Optional",",","default",":","True","."]
code: def __init__(self, space, left=True):
      super().__init__(space=space)
      self.metric_mat_at_identity = gs.eye(space.dim)
      self.left = left
  
imports: import geomstats.backend
  from geomstats.geometry.matrices import Matrices
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.integrator import integrate
  from geomstats.numerics.geodesic import ExpODESolver, LogShootingSolver
  from geomstats.numerics.ivp import GSIVPIntegrator
  from geomstats.vectorization import repeat_out
label_desc: Use image node_id 1 to create a new _InvariantMetricVector object from inherited base classes: RiemannianMetric with example: obj = _InvariantMetricVector(space, left)