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I am trying to work through a book on linear algebra by Serge Lang. I see a whole bunch of rules, formulae, theorems but I don't understand how each of these things are applied in a real world context.

I am studying linear algebra only because I wish to learn machine learning topics.

Is there a book that deals with something akin to 'Applied linear algebra' ? For example , that will explain why exactly we need complicated techniques to decompose and factorize a matrix?

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    $\begingroup$ My favourite linear algebra book is Matrix Analysis by Horn and Johnson. It's not suitable for a first look at the topic though. You might also consider this and this. But there are many basic linear algebra books that might be suitable, e.g. the ones by Gilbert Strang. $\endgroup$
    – mark999
    Commented Sep 26, 2015 at 22:05
  • $\begingroup$ The reason is often speed or numerical stability of calculations. Otherwise there are models that depend upon matrix factorization, in that case the motivation is only the model itself. $\endgroup$
    – Gumeo
    Commented Sep 26, 2015 at 22:09
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    $\begingroup$ Just go through the Gilbert Strang lectures at MIT available for free on-line - a real treat. And I would consider getting his book. $\endgroup$
    – Antoni Parellada
    Commented Sep 26, 2015 at 22:13
  • $\begingroup$ I agree with @AntoniParellada--definitely check out the Strang lectures. In fact, they now have more than just lectures (problem sets, problem videos, tests, etc.). He does mention a lot of applications, though they tend to be centered more around engineering/physics (and not, say, Economics). If you're just starting out then you might want to check out Khan Academy's treatment of Linear Algebra (especially because at MIT the students in Strang's course have already been exposed to vectors, matrices, etc. by the time they take his course). $\endgroup$
    – Steve S
    Commented Sep 27, 2015 at 5:13

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My favourite book on linear algebra is this one. And it's quite inexpensive only 9.99 the kindle version. So related to your question this book teaches linear algebra from practical applications using python working on challenging problems, so some python experience is required though some people have learned python through this book.

Coding the Matrix: Linear Algebra through Applications to Computer Science http://www.amazon.com/dp/0615880991/

enter image description here

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  • $\begingroup$ Great. Is there something like this for R? And not python? $\endgroup$
    – Victor
    Commented Sep 28, 2015 at 16:13
  • $\begingroup$ I'm not sure there is such a book, at least not as high quality as the answers. Universities normally don't teach linear algebra with R. Check this 2013 post about the situation of R and linear algebra blog.revolutionanalytics.com/2013/08/r-and-linear-algebra.html $\endgroup$
    – wacax
    Commented Sep 28, 2015 at 22:49
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Gilbert Strang's linear algebra is good.

If you want to learn linear algebra from scratch I think this one is pretty good too. It is even simpler than Strang's book.

enter image description here

http://www.amazon.com/Linear-Algebra-Applications-8th-Edition/dp/0136009298

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  • $\begingroup$ This books has terrible reviews $\endgroup$
    – Victor
    Commented Sep 28, 2015 at 16:14

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