Another good Linear Algebra book is "Linear Algebra Done Right", which Springer is giving for free right now.
Link: https://link.springer.com/book/10.1007/978-3-319-11080-6
Link: https://link.springer.com/book/10.1007/978-3-319-11080-6
> You are probably about to begin your second exposure to linear algebra. Unlike your first brush with the subject, which probably emphasized Euclidean spaces and matrices, this encounter will focus on abstract vector spaces and linear maps.