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I am starting to learn Linear Algebra but it is has been very mathematical and I don't know its actual usage in programming. I heard it is a very useful subject for movements(animate) and graphics. I thought I could make my learning process for linear algebra more fun if I could learn it from its application through programming. That's learn through the practical way and not just working out on paper.

Since I am still learning the very basics of linear algebra, I am thinking where and how are basic concepts of linear algebra used in programming? What kind of interesting things could be done with basic knowledge of linear algebra such as row-echelon form, LU deposition, linear combination/system, etc. Any tutorials on any languages such as Java, Actionscript, PHP or others teaching the usage of basic linear algebra concepts to create interesting simple things?

Thanks!

Carven
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    Linear Algebra is also used in Artificial Intelligence, when dealing with matrices. It's also used to solve financial problems. Basically, if there's math involved, linear algebra can be useful (or necessary) for solving the problem... –  Jun 19 '11 at 09:45
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    you might find this interesting: [The $25,000,000,000 Eigenvector: The Linear Algebra Behind Google](http://www.rose-hulman.edu/~bryan/googleFinalVersionFixed.pdf) – Nick Dandoulakis Jun 19 '11 at 09:52
  • @xEnON this topic is realated to yours http://stackoverflow.com/questions/1085425/how-is-linear-algebra-used-in-algorithms – Özgür Aug 12 '11 at 14:36

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Matrices and their transformations are used for positioning, rotating and scaling elements in Flash, IOS and Android. Check out transformation matrix wiki, android api, and a cool flash tutorial

Mridul Kashatria
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As you've already stated, the most likely place that you'll find it is in graphics and games programming. You don't say what language you'd like to program in, so I'll assume Java:

http://www.java3d.org/

All techniques are not created equal. You will use LU decomposition and eigenvalues more if you're doing scientific computing.

This is a very good book. Don't be fooled by the date: the mathematics haven't changed. I'd also recommend looking at OpenGL.

duffymo
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  • Thanks for the link! I did said that I prefer to try it with Java, Actionscript, or PHP but I am also opening myself to other languages. But it will be great if the language could be something like Actionscript 3. – Carven Jun 19 '11 at 09:44
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All the simple graphice are made with the use of linear algebra...

Make a new console project nd try your skills...

Genius
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Probably the most important application of linear algebra in programming is Modular Arithmetic.

As for the examples you've provided, the relationship is quite reversed. Programming is used to implement those algorithms, the algorithms are not used for general programming.

Andrei
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    I would consider modular arithmetic to be more closely associated with number theory (or abstract algebra if anything). – jonsca Jun 19 '11 at 10:03