class_docstr: Manifold of lower triangular matrices with >0 diagonal.
  
  This manifold is also called the cholesky space.
  
  Parameters
  ----------
  n : int
      Integer representing the shape of the matrices: n x n.
  
  References
  ----------
  .. [TP2019] Z Lin. "Riemannian Geometry of Symmetric
      Positive Definite Matrices Via Cholesky Decomposition"
      SIAM journal on Matrix Analysis and Applications , 2019.
      https://arxiv.org/abs/1908.09326
class_docstr_tok: ["Manifold","of","lower","triangular","matrices","with",">","0","diagonal",".","This","manifold","is","also","called","the","cholesky","space",".","Parameters","--","--","--","--","--","n",":","int","Integer","representing","the","shape","of","the","matrices",":","n","x","n.","References","--","--","--","--","--","..","[","TP2019","]","Z","Lin",".","``","Riemannian","Geometry","of","Symmetric","Positive","Definite","Matrices","Via","Cholesky","Decomposition","''","SIAM","journal","on","Matrix","Analysis","and","Applications",",","2019.","https",":","\/\/arxiv.org\/abs\/1908.09326"]
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():
      """Metric to equip the space with if equip is True."""
      return CholeskyMetric
  
imports: import geomstats.backend
  from geomstats.geometry.base import DiffeomorphicManifold, VectorSpaceOpenSet
  from geomstats.geometry.diffeo import Diffeo
  from geomstats.geometry.invariant_metric import _InvariantMetricMatrix
  from geomstats.geometry.lie_group import MatrixLieGroup
  from geomstats.geometry.lower_triangular_matrices import LowerTriangularMatrices
  from geomstats.geometry.matrices import Matrices
  from geomstats.geometry.open_hemisphere import OpenHemisphere, OpenHemispheresProduct
  from geomstats.geometry.pullback_metric import PullbackDiffeoMetric
  from geomstats.geometry.riemannian_metric import RiemannianMetric
label_desc: Use image node_id 2 for calling the PositiveLowerTriangularMatrices obj's underlying member method code with example usage: obj.default_metric() and returns: CholeskyMetric