This is an advanced course of “Linear Algebra, I”, and we will take a more abstract view of points on the subjects in linear algebra. That is to say, we will begin with notions of vector spaces and linear maps. They are actually the abstract version of R^n and matrices. Then we will go through different types of vector spaces, like inner product spaces, real and complex vector spaces. Finally, we hope to end up with the studying of operators on the these special vector spaces. This course is the preparation for more advanced courses like “Algebra” and “Functional Analysis”. |