SK Logo

Linear Algebra Done Right

Aug 24, 2020

Not many books intended for math majors are accessible to everyone. The book Linear Algebra Done Right by Sheldon Axler is, however, delightfully comfortable to read. I am not sure why everyone recommends this as a second course in linear algebra. In hindsight, I feel like this could have been my first linear algebra book but perhaps I have recency bias.

Finite v/s Infinite Vector Spaces

Infinite-dimensional spaces have always seemed mysterious but there aren't many special things about them other than some rules from finite-dimensional spaces which break. Here's a few.

  • In general, neither injectivity nor surjectivity alone imply invertibility of linear maps. For finite-dimensional vector spaces, however, one is enough.

  • Only operators on finite complex vector spaces guarantee existence of eigenvalues. See 5.A.18 for an example.

Questions

Here is a list of few questions that I found interesting.

  • 2.A: 16, 17
  • 2.C: 9
  • 3.A: 7, 10, 13, 14
  • 3.B: 22, 23, 29
  • 5.A: 14, 18, 29
  • 5.B: 3,4

Fun

The book has a page numbered 1002100\sqrt{2}.

© 2023 Sanyam Kapoor