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This question already has an answer here:

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

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marked as duplicate by Dietrich Burde, Community Apr 21 '16 at 19:43

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ See also this question. $\endgroup$ – Dietrich Burde Apr 21 '16 at 19:38
  • $\begingroup$ Since you're interested in tensors, you might also like to learn about integration on manifolds. $\endgroup$ – littleO Apr 21 '16 at 19:59
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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

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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.)

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