Linear Algebra Done Right
Some notes from the book.
Table of Contents
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
Infinitedimensional spaces have always seemed mysterious but there arenâ€™t many special things about them other than some rules from finitedimensional spaces which break. Hereâ€™s a few.

In general, neither injectivity nor surjectivity alone imply invertibility of linear maps. For finitedimensional 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 $100\sqrt{2}$.