1. Introduction
Linear Algebra: Infinite-dim Linear Algebra, including some interesting conclusions about linear algebra. Just need required little knowledge of Functional Analysis and Fourier Analysis. The depth is higher than linear algebra, but it does not fully cover the content of Functional Analysis (undergraduate). So it is embarrassing that it is not suitable for exams, only for students who are interested in it.
Why do I always learn some that I don’t take exam, and need to spend a lot of effort to review each time during final exam, and worry about failing the exam?
If nothing else, the next one is a note about Function Analysis, which maybe is in-depth Functional Analysis Topics. Of course, still unsuitable for exams.
2. Textbooks & Lectures
- Analysis II Lecture Notes by Joris Roos UW Madison, Fall 2019
- Matrix Cookbook by K. B. Petersen and M. S. Pedersen
- Linear Algebra Done Right by Sheldon Axler
The first is the main reference book for this Note, is a handout which just over 100 pages. Although the name is Analysis II, the actual algebra is taught with an analytical mind, which requires Calculus, Linear Algebra, and a little of Functional Analysis to understand.
The second is the Matrix Theory lec-note, not undergraduate level (our school didn’t open), less than 100 pages, written very difficult and elegant. It is recommended that future students who want to learn the direction of algebra look at the Matrix Theory and Category Theory are very basic courses.
The third is just about vertor spaces, and I recommend reading it after studying Linear Algebra, it will give you an insight into linear space. You can read a more detailed on Linear Algebra 2 , but now I think Lax’s book is better than LARD in Linear Algebra.
