In today’s G14FUN Functional Analysis lecture I proved Theorem 3.8, that all norms on finite-dimensional vector spaces are equivalent, and they are all complete.
The PIP (picture-in-picture) videos in the corner have improved dramatically now. The lighting is definitely crucial.
Unfortunately, I forgot to turn the mains power on at the wall for the first 3-minute screencast, when I did the recap of where we had got to last time. It is striking how this affects the synchronization and the sound quality.
- Lecture 14, part a (recap of preliminary discussion relating to Theorem 3.8, laptop running on batteries)
- Lecture 14, part b (conclusion of Section 3.2, including the proofs of Theorems 3.8 and 3.10)
February 23 2010