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(i) u+v = v+u

(ii) a(u+v) = au + av

and so on, where u and v are vectors and a is number (real or complex). And I can predict it will mainly talk about mathematical abstraction. But they are just things I already learned in high school, as you guys did. What is so special about u+v = v+u, isn't it obvious. So why do they bother reviewing those things. Well I know there might appear some things rather new later on if I keep reading through it, but just:

1) what good will it do me to study vector space if I know how to deal with vectors?

2) which parts of quantum physics that rely heavily on understanding of vector space, is it so crucial that without having learned vector space I won't be able to get around those parts?

3) is worth for me to spent days to learn this matter?