Maybe Lecture 8 can help us.
https://mediaspace.unipd.it/media/Riunione+Zoom+di+fabio.aiolli%40unipd.it/1_xx81pzmb
if you watch at 1:14:57 the Professor talks about the changing sign
https://mediaspace.unipd.it/media/Riunione+Zoom+di+fabio.aiolli%40unipd.it/1_xx81pzmb
if you watch at 1:14:57 the Professor talks about the changing sign