Appendix B
Basic Linear Algebra
Algebra is generous. She often gives you more than is asked of her.
— Jean le Rond d’Alembert
In this chapter, we will present a very broad overview of linear algebra. More than anything, this is meant to be a refresher. If you would like to learn linear algebra from the basics, we suggest reading Sheldon Axler’s wonderful book [116]. If you are all-in with abstract algebra, we can also recommend the great book by Dummit and Foote [115]. With this out of the way, let’s do some algebra!
When most people think of vectors, they think of fancy arrows pointing in a direction. But, where others see arrows, we mathematicians — in our tireless pursuit of abstraction — see elements of vector spaces. And what is a vector space? Simple!
B.1 Vector spaces
Let be the real or the complex numbers. An -vector space is a set together with an ”addition” function (usually represented by , for obvious reasons) and...
