# Best Books to learn Proof-Based Linear Algebra and Matrices

So I'm in a really serious problem. It's my first year at university and I'm doing a CS major. The math is already getting serious and I'm lost, really lost. It's all about matrices so far and the thing is I really can't do the proofs (of determinants). High school(A-level) was math was pie and it didn't even involve any proofs and that's where I'm lacking now and I'm stressed out. I don't know where to start. So I went online and looked at all the books that have been listed around and here are some I found: Linear Algebra Done Right - Axler Intro. to Linear algebra - Gilbert Strang Linear Algebra - Hoffman and Kunze

These are some, but I'm not sure where to start. I need a book which will teach me some basic proofs and how to think to solve these proofs. So anyone could help me out, where to start?

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## migrated from mathoverflow.netSep 4 '13 at 12:45

This question came from our site for professional mathematicians.

MO is intended for topics at the graduate school level and above. –  Andy Putman Sep 4 '13 at 12:39
Mathstackexchange might get you a good answer. –  Benjamin Steinberg Sep 4 '13 at 12:44
While I don't think it's a duplicate, you may find the answers to the following question useful: math.stackexchange.com/questions/4335/… –  Matthew Pressland Sep 4 '13 at 12:52
I wouldn't use Hoffman and Kunze unless you're already acquainted with mathematical proofs. Besides, it goes beyond just matrices and vector spaces and I would almost consider it a book in abstract algebra. –  neuguy Sep 4 '13 at 12:55
Strange is more computationally oriented although it does have proofs. Intended to some extent for engineers. You can find a very nice set of his videos teaching his course at MIT at their OCW site. Axler is more proof oriented, although starting at a somewhat elementary level. If you want to ever do rigorous math, especially pertaining to LA, Axler is a good place to expend some effort. –  Andrew Sep 4 '13 at 17:38

There is a HUGE amount of Linear Algebra books. Let me point out just two:

• Noble, Daniel, Applied Linear Algebra. Prentice Hall.
• Lancaster, Tismenetsky, The Theory of Matrices. Academic Press.

I would suggest the first one for a beginner and later on you can take a look at the second one. Enjoy!

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Elementary Linear Algebra by Larson. There are basic proofs and also exercises called "guided proofs" that help with initial intuition and explain why you are doing the steps. There are lots and lots of problems to solve but the proofs are there as well and they are not of high mathematics. Axler is good too but requires a bit more foundationally.

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$174,66!! amazon.com/Elementary-Linear-Algebra-Ron-Larson/dp/1133110878 Are you kidding me? Is the world getting crazy or what? – a.r. Sep 4 '13 at 17:33 I definitely didn't pay that much! And I would say if that is the going rate, then don't go that route. I payed 3 years ago about$50 for a used copy. –  Eleven-Eleven Sep 4 '13 at 19:12
Larson doesn't seem to have enough proofs to serve as an introduction to the latter. I'd rather get some slow-paced introduction tailored for pure mathematicians in the OP's place. –  darij grinberg Aug 16 '14 at 12:17
I know it's not an introductory book, but Hoffman and Kunze's Linear Algebra is free in the internet now.... –  Eleven-Eleven Aug 17 '14 at 23:54