function P = GenerateHouseholder(a, pad)
alpha = -sign(a(2))*norm(a(2 : end), 2);
r = sqrt(0.5*alpha*(alpha - a(2)));
v = zeros(length(a), 1);

v(2) = 0.5*(a(2) - alpha)/r;
v(3 : end) = 0.5*a(3 : end)/r;

v = [zeros(pad, 1); v];

P = eye(pad + length(a)) - 2*(v*v');
end