The branch of mathematics I understand the most. The only book I read to get good in Linear Algebra is this one.
May write my own linear algebra book, some ideas and directions it can go are down below.
The basics are pretty much covererd in the first six chapters of the above mentioned book. The author, after the first six chapters goes to showing some practical implications of linear algebra. There are few points to consider :
- The overall approach: geometric or abstract.
- Geometric may be more intuitive and beginner friendly, but fails when things get more advanced/abstract.
- Abstract view may not have been used in real life, yet.
- Some practical applicatins.
- Quantum Physics/Computing
- Deep Learning
- Representatin theory
- Engineering (FFT)
- Exercises, something I always struggled with in a math book
- Quality vs Quantity (mostly the former ofc)
- Programming questions (MATLAB, openBLAS)
- Higher linear algebra
- Explore and inttroduce how graduate and post graduate level LA looks like
- Explrore some domains
- Papers that recently came out, and are interesting