I got my hands on a copy of the Second Edition of the text but noticed that the Preface to the Instructor and Preface to the Student start with “ You are probably about to teach a course that will give students their second exposure to linear algebra. During their first brush with the subject, your students probably worked with Euclidean spaces and matrices. In contrast, this course will emphasize abstract vector spaces and linear maps.“ (emphasis mine) and “You are probably about to begin your second exposure to linear al- gebra. Unlike your first brush with the subject, which probably empha- sized Euclidean spaces and matrices, we will focus on abstract vector spaces and linear maps... This book starts from the be- ginning of the subject, assuming no knowledge of linear algebra.” (emphasis mine) respectively.
The thing is, I have no idea of what a Euclidean space is. In our high school curriculum, we were taught vectors and matrices as separate concepts, though vectors did involve some determinants.
So in matrices we were taught things like matrix multiplication, adjoint, inverse, (involutory, idempotent, nilpotent, orthogonal) matrices, determinant evaluation with row and column operations, and how to solve systems of linear equations in three variables using adjoint method/determinant method on AX=C. (No eigenvectors)
While in vectors we were taught basically the geometrical aspect, and scalar and vector triple products. (No span/basis etc.)
So, my question is, will Axler’s book be well-suited to me? Or should I read up something more basic?
I also noted a few mentions of Hoffman and Kunze’s book, which, in this link is supposed to be for people of the level of completing Spivak. I have just started with Spivak (Basic Properties of Numbers), so should I stay away from it ?