Houjun Liu

Axler 2.A

Key Sequence

New Definitions

Results and Their Proofs

Questions for Jana

  • obviously polynomials are non-linear structures; under what conditions make them nice to work with in linear algebra?
  • what is the “obvious way” to change Linear Dependence Lemma’s part \(b\) to make \(v_1=0\) work?
  • for the finite-dimensional subspaces proof, though we know that the process terminates, how do we know that it terminates at a spanning list of \(U\) and not just a linearly independent list in \(U\)?
  • direct sum and linear independence related; how exactly?

Interesting Factoids

I just ate an entire Chinese new-year worth of food while typing this up. That’s worth something right