% Returns 1 if the matrix is Toeplitz + Hankel
% AND if all functions of the matrix are Toeplitz + Hankel.
% Returns zero otherwise.
function pass_test = strongTplusHtest(A)
N = size(A,1);
% simply hope that the matrix is diagonalizable
pass_test = true;
[V , D] = eig(A);
for j = 1:N
    v = V(:,j); 
    M = v*v.'; 
    pass_testj = TplusHtest(M);
    pass_test = pass_test & pass_testj;
end
