So I'm a college student that has taken 3 semesters of calc/diff eq/linear algebra and I think linear algebra has been by far my favorite course so far and I would love to know more in the subject, the style of a consistent theorem/proof approach really appealed to me. So I ask what is a good book or resource to learn more advanced linear algebra or should is there other subjects I need to come to grips with first?
specifically I'd like to become more familiar with metrics/tensors
Given your level, I would say that an excellent book would be "Linear Algebra Done Right" by Axler. His book is less computational than most and a great second proof-based course in LA. http://www.amazon.com/Linear-Algebra-Right-Undergraduate-Mathematics/dp/3319110799/ref=sr_1_1?s=books&ie=UTF8&qid=1461267526&sr=1-1&keywords=linear+algebra+done+right
But, perhaps you want something even more challenging, in which case, I'd recommend "Linear Algebra" by Hoffman and Kunze. http://www.amazon.com/Linear-Algebra-Edition-Kenneth-Hoffman/dp/0135367972
Without a doubt, "Linear Algebra" by Serge Lang.
(A note of caution-there is also "'Introduction to Linear Algebra" by Lang-a fine book by itself, but from your question, you are looking for a more advanced text, like the first.)
