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I am looking for suggestions, it has to be a self study book and should be able to relate to applications to real world problems. If it is more computer science oriented , that would be great.

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Have you searched for similar questions here? They have been answered with numerous, well-detailed recommendations. –  Andrew Apr 18 at 22:08
    
yeah, but i was looking more from Computer science perspective. –  bcp Apr 18 at 22:09
    
Maybe the best book for Computer Science is just the best book at all, in that case I would recommend Hoffman's Linear Algebra. –  Jonas Gomes Apr 18 at 22:31
    
This question is relevant. –  Yuri Vyatkin Apr 18 at 23:11
    
Strang, whose book s mentioned below, has free video lectures of his course at MIT Open Courseware. This is the more "practical" LA course at MIT. On the more theoretical side, They tend to use Axler, "Linear Algebra Done Right." –  Andrew Apr 18 at 23:28

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Linear Algebra and its Applications by David C. Lay is a simple book containing many references to real-world problems, including computer science.

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Linear Algebra and its Applications- Gilbert Strang seems to be very recommended.

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I love this book, but the $270 price tag on Amazon induces a bit of nerd rage. The pdf can be found online. –  littleO Apr 18 at 22:46
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You can get a 3rd edition of this book used for cheap if you buy the international edition: textbookrush.com/search/… Even though the price tag is $270, there are cheaper options. –  ml0105 Apr 18 at 22:54

There is an innovative course Coding the Matrix offered by Philip Klein which consists of a book and a course offered on Coursera and other places. It even has a Twitter account for keeping updated. The reviews are controversial, see also here and here, but it looks as an interesting challenge to try. It is designed, according to the author's website, as a "course is to provide students interested in computer science an introduction to vectors and matrices and their use in CS applications".

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Jim Hefferon has a freely available book Linear Algebra that discusses various applications as well as giving a solid theoretical base.

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Strang revisited with a valid free download:

https://archive.org/details/flooved1323

"Computational Sciences and Engineering - Applied Linear Algebra"

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