# Linear Algebra Done Right

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 $100\sqrt{2}$.