Ok HN, what's the best book for learning this stuff? My criteria are: rigorous is good, but so is fun. Bonus points for anything a hacker would appreciate, such as computational applications or exercises.
Link to the course: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-...
Link to the YouTube videos of the lectures: http://www.youtube.com/watch?v=ZK3O402wf1c&feature=resul...
http://www.amazon.com/Introduction-Linear-Algebra-Fourth-Gil...
You can find a free PDF version online.
I like it more then Strang because it's a lot more concise, covers some more advanced topics and unlike Strang everything is said very accurately. I think Strang's rather hand-wavy way of explaining things starts faltering when he talks about more advance topics.
I would read Strang and listen to his lectures to get a good feel for Linear Algebra (to build up the intuition), and if you feel like you want more then pick up Meyer's book
Amazing writing, very succint & hacker-friendly.
Link to lectures and materials: http://see.stanford.edu/see/courseinfo.aspx?coll=17005383-19...
* http://www.youtube.com/view_play_list?p=F706B428FB7BD52C
* http://www.youtube.com/view_play_list?gl=DE&hl=de&p=...
based on the book of the same name. This is one of "name 5 books you would take with you on a desert island" kind of books, a beautiful work of art.
For numerical aspects of linear algebra (and other subjects), I've found Numerical Recipes to be quite helpful.
From the book's intro:
>But, suppose we asked a professional mathematician to step back a bit from his habitual way of speaking and write in a more linear fashion? And suppose we even asked more, for example, that he make his writing lively? ... The purpose of this book is to furnish the reader with the first mathemat- ical tools needed to understand one of the pillars of modern mathematics, i.e. linear algebra. The text has been written by a mathematician who has tried to step out of his usual character in order to speak to a larger public. He has also taken up the challenge of trying to make accessible to everyone the first ideas and the first techniques of a body of knowledge that is fundamental to all of science and technology.
As others have suggested, something like Golub and Van Loan is a better choice. The technical notes to go with the LAPACK library, and similar documents from those developing related software, are also likely to be of interest to anyone doing this stuff seriously.
The recommendations given here so far are for intro/abstract linear algebra texts.
Texts that emphasize coordinate-free approaches, like Linear Algebra Done Right, don't really get at the numeric computations issue.
http://matrixeditions.com/UnifiedApproach4th.html
which is theoretical and linked to other subjects of higher math, but by no means slights practical problems or numerical methods.
http://www.amazon.com/Computations-Hopkins-Studies-Mathemati...
This is the "how we wrote Lapack" book.
For those who are just starting on this subject, I highly recommend that you rework the proofs for the bounds between the various matrix norms [1]. These bounds are the building blocks for most interesting analyses in matrix computations. And understanding these analyses are essential if you want to know which algorithm will work best for your problems.
[1]: http://en.wikipedia.org/wiki/Matrix_norm#Examples_of_norm_eq...
(I just bought the Strang book mentioned downthread).
Edit: Let's see if this works: http://news.ycombinator.com/edit?id=2993321.
Everyone I talked to then recommended the Strang textbook, and also Stanford EE263, both already pointed out by other commenters here.
Start here: http://www.catonmat.net/blog/mit-linear-algebra-part-one/