SK

Linear Algebra Done Right

Date written Aug 24, 2020
Filed under Linear Algebra in math

Contents
  • Finite v/s Infinite Vector Spaces
  • Questions
  • Fun

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}.