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.
I highly recommend the MIT 18.06 open course on linear algebra - the lectures are first rate. I've been going through this as a refresher, in prep for the Stanford machine learning class.
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
Thirded. We used an earlier edition at my school for Linear Algebra, and in spite of having a Professor who was retiring at the end of the class (complete with "I'm getting too old for this shit" demeanor), the book was approachable enough for us to get by.
How much time do you have ?
You can easily spend several years and get multiple PhDs in linear algebra, but if you only have half an hour to devote to this, I strongly suggest Leduc's Cliff Notes.
http://www.amazon.com/Linear-Algebra-Cliffs-Quick-Review/dp/...
The (free, open) stanford class ee263: Linear Dynamical Systems is really good. It concentrated on how to take real problems and fit them into a form where a computer can solve them in what appears to be complete magic. Plus Stephen Boyd is a very entertaining lecturer. This article reminds me a lot of his asides.
While Numerical Recipes has certainly earned its place in the history of the genre, it is only fair to point out that it is very out-dated by now, and that the example code is neither particularly well-written (from a software development point of view) nor freely usable in your own projects.
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.
I've heard good things about this one, as well as _Linear Algebra for Everyone_. http://amzn.com/8847018382
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.
Yes, Golub/van Loan is the bible. But Walkins's "Fundamentals of Matrix Computations" (http://www.amazon.com/o/asin/0470528338/) is much more accessible to self-learners.
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.
I'm in. Which of the Strangen? And what's a suitable forum for working out the details and proceeding? A Google group would probably be my go-to default but I'm open to alternatives.
I bought _Linear Algebra and its Applications_, but as I'm fond of reminding people on HN (come work for us!) my book budget is unbounded, so I'm happy to buy a different one.
