def orthogonal_complement(C, tol=1e-5):
    """ Computes the orthogonal complement to a given matrix proj"""
    xnp = get_library_fns(C.dtype)
    _, S, VH = xnp.svd(C, full_matrices=True)
    rank = (S > tol).sum()
    return VH[rank:].conj().T
 Computes the orthogonal complement to a given matrix proj
cola/linalg/tbd/nullspace.py