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
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docstr: Check if mat is lower triangular with >0 diagonal.
  
  Parameters
  ----------
  point : array-like, shape=[..., n, n]
      Matrix to be checked.
  atol : float
      Tolerance.
      Optional, default: backend atol.
  
  Returns
  -------
  belongs : array-like, shape=[...,]
      Boolean denoting if mat belongs to cholesky space.
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code: def belongs(self, point, atol=gs.atol):
      """Check if mat is lower triangular with >0 diagonal.
  
      Parameters
      ----------
      point : array-like, shape=[..., n, n]
          Matrix to be checked.
      atol : float
          Tolerance.
          Optional, default: backend atol.
  
      Returns
      -------
      belongs : array-like, shape=[...,]
          Boolean denoting if mat belongs to cholesky space.
      """
      is_lower_triangular = self.embedding_space.belongs(point, atol)
      diagonal = Matrices.diagonal(point)
      is_positive = gs.all(diagonal > 0, axis=-1)
      return gs.logical_and(is_lower_triangular, is_positive)
  
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 4 for calling the PositiveLowerTriangularMatrices obj's underlying member method code with example usage: obj.belongs(point, atol) and returns: gs