class_docstr: Class for PSD(n,k).
  
  The manifold of Positive Semi Definite matrices of rank k: PSD(n,k).
  
  Parameters
  ----------
  n : int
      Integer representing the shape of the matrices: n x n.
  k : int
      Integer representing the rank of the matrix (k<n).
class_docstr_tok: ["Class","for","PSD","(","n",",","k",")",".","The","manifold","of","Positive","Semi","Definite","matrices","of","rank","k",":","PSD","(","n",",","k",")",".","Parameters","--","--","--","--","--","n",":","int","Integer","representing","the","shape","of","the","matrices",":","n","x","n.","k",":","int","Integer","representing","the","rank","of","the","matrix","(","k","<","n",")","."]
code: def __init__(self, n, k, equip=True):
      if not k < n:
          raise ValueError("k must be lower than n")
  
      super().__init__(
          dim=int(k * n - k * (k + 1) / 2),
          shape=(n, n),
          equip=equip,
          default_coords_type="extrinsic",
      )
      self.n = n
      self.rank = k
      self.sym = SymmetricMatrices(self.n, equip=False)
  
imports: import geomstats.backend
  from geomstats.geometry.fiber_bundle import FiberBundle
  from geomstats.geometry.full_rank_matrices import FullRankMatrices
  from geomstats.geometry.general_linear import GeneralLinear
  from geomstats.geometry.manifold import Manifold
  from geomstats.geometry.matrices import Matrices, MatricesMetric
  from geomstats.geometry.quotient_metric import QuotientMetric
  from geomstats.geometry.spd_matrices import SPDEuclideanMetric, SPDMatrices
  from geomstats.geometry.special_orthogonal import SpecialOrthogonal
  from geomstats.geometry.symmetric_matrices import SymmetricMatrices
label_desc: Use image node_id 1 to create a new RankKPSDMatrices object from inherited base classes: Manifold with example: obj = RankKPSDMatrices(n, k, equip)