For anyone watching this who doesn't feel like they are completely getting the concept, Prof Strang has an updated lecture in 18.065 on the SVD, which I think lays it out in a cleaner way: https://youtu.be/rYz83XPxiZo####[['Prof Strang', 'Instructor', 'POS'], ['lecture', 'Course_General_Feedback', 'POS']]