function zerobasmat = zerobasis(k)
%  sets up a k by k-1 matrix with orthonormal columns
%  using the first k non-constant fourier basis function
%  values at 0.5, ..., k-0.5
tk = (0:k-1) + 0.5;
fbasis     = create_fourier_basis(k,k);
fbasmat    = eval_basis(tk, fbasis);
fbasmat    = fbasmat(:,2:k);
fbasnorm   = sqrt(sum(fbasmat.^2));
zerobasmat = fbasmat./(ones(k,1)*fbasnorm);



