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I recently took an introductory class on linear algebra (covered solving linear systems, determinants, eigenvectors, diagonalization, some vector spaces, basis and combinations, transformations etc.)

Since it was a class for engineering students, it was mostly going through the motions without any insight - felt very mechanical and repetitive. However, I want to get a deeper understanding of the material, how it relates to vector spaces, geometry etc. For this I'd like a textbook recommendation.

Keep in mind I'm just a second-year undergraduate in engineering, so something rigorous might go over my head. Thanks!

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    $\begingroup$ Wow, @HasanSaad, get over yourself. $\endgroup$ – Paul May 26 '15 at 14:52
  • $\begingroup$ @HasanSaad Some people don't have rigorous backgrounds and everyone learns at different rates. It would be nice if you take this into account when commenting on someones situation; your current comment comes across (IMO) as arrogant and certainly not helpful to the OP. $\endgroup$ – Rammus May 26 '15 at 14:52
  • $\begingroup$ Welcome to Math.SE! Can you expand a little bit more on what sort of book you are looking for: to me there is not much to be found between the type of book you have been learning from until now and books that treat linear algebra in a "rigorous" way. $\endgroup$ – Hrodelbert May 26 '15 at 14:54
  • $\begingroup$ "Rigorous" might not have been the best choice of wording. I want a more complete treatment of the math, so I guess I do want the rigorous proofs and such. What I don't want is something that only presents the the proofs with no accompanying explanations, as I find I'm often unable to understand the more "concise" textbooks. So ideally I'm looking for something that's thorough, but also intuitive. My main problem with the course I took is that I did really well, but I felt like it was just memorizing rules. $\endgroup$ – TRPLBLK May 26 '15 at 15:39
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I personally do not think it is ideal to try to learn linear algebra from one text. My personal favorite text is the one by Gilbert Strang. It is very good at the conceptual aspects of the subject, and in particular focuses on abstract topics starting as early as chapter 2. By contrast, the main other text that I am familiar with, by David Lay, sticks to essentially computational topics until chapter 4 (although to be fair chapter 3 is rather short).

The downside to this is obvious: Strang's treatment of the basics, while well-written, is relatively terse. As a result, I think most students will struggle if they start with Strang. So I would suggest starting with another text (I really don't have a recommendation; I found Lay's book adequate but not excellent) and then moving on to Strang when you have grasped the basics.

I especially think Strang would ultimately be good for you in particular because you mention that you want more explanation rather than conciseness. Strang definitely provides that, with a lot of expository paragraphs in each chapter (except the first).

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  • $\begingroup$ Thanks. I was recommended Strang a year ago, and didn't understand it very well, because I hadn't taken any courses in Linear Algebra yet. Now that I know the basics I'm going to come back to Strang and see if it makes more sense now. $\endgroup$ – TRPLBLK May 26 '15 at 15:47
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This is not really an answer, more like a long comment:

If my memory doesn't fail me, Serge Lang's Linear Algebra is a nice book, covering topics in an intuitive manner, without entirely leaving rigour aside. Personally though, I read Hoffman & Kunze's Linear Algebra during the course I took last semester. It is more rigorous, and probably slightly less intuitive, however it does cover topics more profoundly, and it has some really mind blowing proofs.

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I found that the Ron Larson book, "Elementary Linear Algebra", provided good proofs for the material. I know you can pick it up on Amazon, but if you look there may be some free-er copies floating out on the web.

You should also Google Scholar search for linear algebra papers and other proofs for more in depth knowledge.

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  • $\begingroup$ Welcome to math.SE! I'm unfamiliar with the details of textbook press, but did you know that prof. R. Larson is alive and most likely willing to get a monetary income from his work? $\endgroup$ – user228113 May 26 '15 at 15:09
  • $\begingroup$ @G.Sassatelli I personally always purchase copies of textbooks from legitimate sources. However, I have also seen that older editions of the same text book can be obtained cheaply if not freely from some sources. $\endgroup$ – J-Eubanks May 26 '15 at 15:17

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