docs: def is_transition_matrix(T, tol=1e-12):
      r"""Check if the given matrix is a transition matrix.
  
      Parameters
      ----------
      T : (M, M) ndarray or scipy.sparse matrix
          Matrix to check
      tol : float (optional)
          Floating point tolerance to check with
  
      Returns
      -------
      is_transition_matrix : bool
          True, if T is a valid transition matrix, False otherwise
  
      Notes
      -----
      A valid transition matrix :math:`P=(p_{ij})` has non-negative
      elements, :math:`p_{ij} \geq 0`, and elements of each row sum up
      to one, :math:`\sum_j p_{ij} = 1`. Matrices wit this property are
      also called stochastic matrices.
  
      Examples
      --------
      >>> import numpy as np
      >>> from msmtools.analysis import is_transition_matrix
  
      >>> A = np.array([[0.4, 0.5, 0.3], [0.2, 0.4, 0.4], [-1, 1, 1]])
      >>> is_transition_matrix(A)
      False
  
      >>> T = np.array([[0.9, 0.1, 0.0], [0.5, 0.0, 0.5], [0.0, 0.1, 0.9]])
      >>> is_transition_matrix(T)
      True
  
      """
      T = _types.ensure_ndarray_or_sparse(T, ndim=2, uniform=True, kind='numeric')
      if _issparse(T):
          return sparse.assessment.is_transition_matrix(T, tol)
      else:
          return dense.assessment.is_transition_matrix(T, tol)