def belongs(self, mat, atol=gs.atol):
"""Check if a matrix is symmetric with positive eigenvalues.
Parameters
----------
mat : 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 is an SPD matrix.
"""
is_sym = self.ambient_space.belongs(mat, atol)
is_pd = Matrices.is_pd(mat)
belongs = gs.logical_and(is_sym, is_pd)
return belongs
