Most universities have studen license servers for Matlab afaik. And, Matlab is really really, annoyingly powerful. You've got almost anything to try your ideas, implement an academic paper. But, it is slow (execution time).
Prototype with Matlab, implement with C++. That's what I usually prefer. I am not a Python expert, just learning it. but I think it will be slower than C, and less powerful than Matlab, from my perspective of working.
I think you'd be surprised at how powerful NumPy is. Try timing multiplying large matrices (I can tell you who wins, and not by a small margin)
One downside is you do have to poke around for the right functions, whereas in Matlab you have all the functions sitting in your (always global) namespace.
We use python for pretty much everything in my research group -- high-level scripting of simulations written in C; controlling experiments over serial, GPIB, usb; and data analysis and plotting for publications. I used Matlab for several years prior, but got really annoyed by the limits of the language when you try to do anything beyond matrix manipulation. Python + scipy + pylab is a pretty effective replacement for matlab prototyping and data analysis, with a much better general purpose language and FFI. Anything that needs to be fast you can write in C/C++ and wrap with swig or ctypes so that you can still use a high-level language to run all your simulations, and do the data analysis as well.
Prototype with Matlab, implement with C++. That's what I usually prefer. I am not a Python expert, just learning it. but I think it will be slower than C, and less powerful than Matlab, from my perspective of working.