If you've ever done anything with matrices (and are lazy) you should have encountered Matlab. And if you haven't, it's worth checking out. Matlab made my life so much easier!
Python, because I know it already, and its my day to day language. As far as I know it has decent libraries.
GNU Octave, as it was reccomended on the Coursera course.
R as it is an open source alternative, no expensive licensing cost, so I can try it out a no risk.
Would I gain anything going to Matlab, as I can see advantages with the others being open source?
"One of the biggest new features for the Octave 3.8.x release series is a graphical user interface. It is the one thing that users have requested most often over the last few years and now it is almost ready."
If you're planning on spending more than a few hours in the tool, consider spending the $200 on the one that's from this century.
I picked up Matlab late and wish I'd done so sooner. It's a REPL for higher-level thinking and quick experimentation. It makes some hard things very very simple and some simple things very hard. They've dropped the price and fixed a lot of shit in the last 5 years. It's replaced a lot of goofing around in Python and Excel for me.
Edit: I have a love/hate relationship with R and more of a love relationship with Python but they don't do ANYTHING like what Matlab does.
http://en.wikibooks.org/wiki/MATLAB_Programming/Differences_...
Love open source, glad they're doing it, much love to the devs -- and life is just too fucking short. If you're broke or screwing around--ok, maybe. If you're sitting in it more than an hour a week, maybe Photoshop is worth the $10/month vs GIMP, dig?
And if you're in school and get it for free or are interested in getting up to speed with the state of the art in machine learning and qualify for the personal license at under 200 bucks? I can't think of a better tool.
I've used both before. Matlab in my CompSci BS and MS and Octave in my professional career.
I'm just making the point that your critique of Octave seems a little harsh, and to the Leyman skews the reality - that Octave is an open source alternative. Yes, a little rough around the edges if you intend to use the visual aspects of the tool, but for matrix multiplication etc it has its use cases.
The parts you say are good about Octave are EXACTLY the stuff I use Python and R for. If you want to use a Matlab library or toolkit, maybe cut in paste some code from a paper, do a quick 'what if' thing -- Octave just doesn't cut it.
(My point in speaking up here isn't to diss Octave it's to re-center the reality around Matlab.)
I've not used Matlab but I've used Octave (during the ml class from Andrew Ng) and it wasn't too awful. Occasionally very frustrating though so if Matlab solves those frustrations I could see it being worth it if you're going to spend time in it!
That being said Matlab is a pretty poor language for anything beyond prototyping and testing proofs of concept. And when I'm doing anything that might turn out become a longer lived project I always choose Python and numpy.