I really appreciate this reply, since this is something I've always been curious about. If you have time, I would really appreciate it if you could elaborate on this point (maybe with some equations), but you've already given me a ton to think about, thank you!
Also, is the new basis orthogonal to the original, or just another orthonormal basis? I don't see why it would be orthogonal to the original.
Also, is the new basis orthogonal to the original, or just another orthonormal basis? I don't see why it would be orthogonal to the original.