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I intend to study linear algebra during my summer vacation.I will be thankful if anyone could please point me to a good text.I do not care about the difficulty as long as the book is self contained.I do have some experience with problem solving and proof-writing.

Edit:I don't care about applications.I prefer one which is quite theoretical. Secondly,here is a book I came across.I request comments on that book too.I will make a choice after some deliberations.

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The answer depends on what you wish to do with your Linear Algebra knowledge. If you want to apply it to engineering, use Poole/Lay/Strang. They majorly deal with Applied Linear Algebra. If you want to get into Numerical Computing, get Golub and Loan. If you want to explore the theoretical side, get Hoffman and Kunze. Having said that, there are so many books for LA that you can find exactly the one you want if you do a little searching. –  Inquest May 11 '12 at 15:09
    
@Nunoxic I prefer a theoretical one. –  user31029 May 11 '12 at 15:29
    
There is a lovely little book "Abstract Linear Algebra" by Curtis if you have a little experience with modern algebra this book will be easy to read and quite rewarding. –  Bill Cook May 11 '12 at 18:30
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up vote 5 down vote accepted

I asked the same question a few days ago on the chat rooms, and there seems to be some consensus over the following texts:

  1. Linear Algebra 4th edition - Friedberg: This book is particularly focused on theory, with little to no examples that are taken from other fields (such as computer science). However, if you fully understand it, you should be able to apply any of the concepts yourself. It is a pretty challenging text, maybe one of the richest ones. So this should be a good bet.

  2. Hoffman/Kunze Linear Algebra

  3. Axler's Linear Algebra

  4. Strang's Linear Algebra Applications and Introduction - This is a good book for applications to engineering, etc. It is the book they use for the MIT OCW course.

These should be good books to get you started right away. However, also make sure to check out online resources and videos, such as MIT's OCW material on L.A, and other easier reference guides such as Paul's notes. There are plenty of online pages that were put up by courses at many different colleges, so you are bound to certainly find tons of materials, such as notes, homework problems, exams, etc.

EDIT (links): Berkeley, MIT (theoretical)

Hope this helps.

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These are brilliant books for Theoretical LA but are we sure the OP is asking for books with a theoretical flavor? –  Inquest May 11 '12 at 15:12
    
Hi Nunoxic. I added Strang. I think that one complements well with engineering applications. EDIT: I also see that you chose it too! –  Nico Bellic May 11 '12 at 15:15
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