Completeness and equivalence of norms on finite-dimensional spaces

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)

Joel Feinstein

February 23 2010

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