nice question; i think some may claim because MATLAB has so many libraries and so, it makes your life much easier to develop your simulations/researches with it but the same could be said about C++ or Python!(they come with batteries included too+0$+open); my hypothesis is that popularity of MATLAB is there because it reached a point at which a great part of the scientific community used (their mind is imprinted) to be using it for their works over many years then similar things are no match for it anymore(it made it sticky i suppose); i mean because somehow professors used it then their pupils used it too~ kinda cascading(randomly, as MATLAB as the seed) but it could be something else;

in short because people happened to need a software for their researches (to run simulations, to plot, etc) AND MATLAB WAS THERE AT THE RIGHT TIME IT STUCK!

it's just a hypothesis; so no proof yet!;0)

nice question; i think some may claim because MATLAB has so many libraries and so, it makes your life much easier to develop your simulations/researches with it but the same could be said about C++ or Python!(they come with batteries included too+0$+open); my hypothesis is that popularity of MATLAB is there because it reached a point at which a great part of the scientific community used (their mind is imprinted) to be using it for their works over many years then similar things are no match for it anymore(it made it sticky i suppose); i mean because somehow professors used it then their pupils used it too~ kinda cascading(randomly, as MATLAB as the seed) but it could be something else;

in short because people happened to need a software for their researches (to run simulations, to plot, etc) AND MATLAB WAS THERE AT THE RIGHT TIME IT STUCK!

it's just a hypothesis; so no proof yet!;0)

I don't not what to think about "imprinting". If it was done on purpose by a company, it's not too good. Although Microsoft has been doing it for a long time...

I believe the graphics part of Matlab is a strong selling point. I could choose to program in C++ and get the results faster but with Matlab you have publication quality graphics, including tables you can include in your publications. 

Matlab has a Student Version that is much cheaper, and comes with all the libraries. But I think it offers both a Swiss Army Knife mentality and good graphics.

Matlab is offered at very low prices to universities, also students are encouraged to download and install students version of matlab. Matlab  also provide a huge selection of ready made libraries (free and non free) to accomplish several computing end visualization task. It is possible to use Scilab or Octave as an alternative to it also if you want to use matlab programs or syntax.

Beside all answers, I think programming with Matlab is easier for people. Specially those who are not real programmer. Matlab is a 4 level language.

Although i have never used MATLAB for any research purpose yet(but i am familier with MATLAB) just because i am programmer i and i have good command over other programming language which allows me to implement my program in those languages. But with MATLAB as it provides a good visualization and a lot of libraries to implement your idea even if you and not a programmer you can easily implement your idea. That means you will spend more time on polishing your idea than spending time on how to program the idea.

I haven't read other people's answers so sorry for repetition. But here's my take. In one line, it can be said that MATLAB saves time!  Of course there are tons of free and maybe faster and more reliable softwares and programming languages out there, but Matlab's expensive for a good reason - these guys have put tons of effort into making programming easier, especially for non-CS types. No wonder you see most EE and ME and Chem. and what-not-field students and researchers use Matlab for their research. Matlab helps you implement your theories in a quick and efficient manner so that all you need to worry about are the underlying principles of your algorithms.

Being from a CS background I've programmed in C,C++,Java, Python but nothing is easier than Matlab. And I hear people say "it makes you lazy"; well that may be true to some extend; but as PhD student I would like to implement and test out my ideas in a quick manner to validate them, instead of wondering whether my memory allocation technique is resulting in segfaults all the time!

I have something to mention in this issue.

1) MATLAB has a straight-forward, clear and well demonstrated interface for error, help and demos. Error messages and help demonstrations are awesome.Compared to C (at least) MATLAB is a far better choice in this respect. One oneself can learn it if the basics of data types and array (just the definition will suffice) are clear. This is the greatest advantage of using MATLAB.

2) Practically speaking, it is not the must that all researchers and students must be good programmers, other things are important too... Good programming knowledge will help, but, a one requires a quick review and understanding of the concepts, and most of the time he/she needs to repeat the results, solve equations, view fields or graphs, and in all such cases he/she is often much important than gaining knowledge about the computational time, complexity, memory related issues, libraries and other sort of issues for minor improvement in accuracy. Moreover, anyone in any field can understand and use it easily, because tools and codes are day by day updated to extend the scope of MATLAB in different fields of study and daily work. A specialist may need other softwares or expertize in programming, but till then MATLAB is for all.

If you are well proficient in MATLAB and you have no problem doing your applications in MATLAB then why would you switch over to something else like PYTHON etc. Writing code in C or C++ is quite time consuming as compared to MATLAB

I think MATLAB is superb for digital image processing.  You can write the essential drawing and display scripts within a few lines.  Makes it easier to experiment without needing to set up as much as in a traditional programming language.  Very good for applied research.  One other benefit of MATLAB is the MATLAB File Exchange, a way to grab more source code, packages, or applications.  http://www.mathworks.ca/matlabcentral/fileexchange/

Not to mention it is a place that you can upload your own work, and share your research.  

I think MATLAB saves your time to check your idea especially in your publications in comparison to C/C++ or python. On the other hand, if you are expert to writ your idea in matrices form, then MATLAB also can be fast.

I have extensively used Matlab in my research work. Another key point to mention is that not only provides a friendly framework to matrix computation, but it also provides a great framework to learn different topics that greatly speed up the learning curve. 

Matlab is made for codes prototyping (and of course linear algebra calculation). But it has also a long history and what made it so successful is also its extensive toolboxes. Ok you can have the same with open source software, but as far as I know, none of them have both that much of toolboxes and that much of flexibility.

If I have to ditch matlab I would go for python, because it offers almost the same flexibility for code prototyping but still it is often more painful than using matlab just because of all these libraries inclusion.

And this popularity is not recent, plenty of colleagues working in electrical engineering are using matlab since decades and this is also true for many research fields other than electrical engineering.

I do suspect it's largely because of programming language inertia - people tend to cling to what's already familiar.

Python (through SciPy modules, http://www.scipy.org/) at the moment offers pretty much the same functionality as MATLAB, is free, easy to learn and use, and has very active community.

Here are Python's alternatives to MATLAB features:

• "publication quality graphics", "essential drawing and display scripts within a few lines" - matplotlib, http://matplotlib.org/
• "straight-forward, clear and well demonstrated interface" - IPython, http://ipython.org/
• linear algebra; matrix calculations: NumPy, http://www.numpy.org/

There are also Python modules for symbolic algebra (SymPy, http://sympy.org/en/index.html) and for data analysis (Pandas, http://pandas.pydata.org/), but these can be seen more as alternatives to Mathematica and R, respectively.

I find Matlab incredibly useful for research, mainly because of the speed in terms of development time, which is far more important in research than when developing commercial software where it's worth spending weeks refining code to shave off a couple of seconds processing time. It lets me get on with solving a problem without wasting time with details of the programming language, the simple and powerful plotting tools help me visualise what the code is doing, excellent error handling in the development environment and the vast library of functions developed by experts in their field.

MATLAB with its Simulink and other toolboxes are nicely integrated and fully supported (Manual, Help, etc) and make a user-friendly environment. These are all every serious researcher/programmer may dream to have in one package.

Abdul you say it's the best, in which sense?

I agree that MATLAB and Octave are great for quick prototyping, matrix operations, and plotting. To help the community, I've built a MATLAB-Octave API fiddler. It is www.SaturnAPI.com. You can use it to quickly test your scripts, and you can also turn it into a RESTful API for use in your external apps.

https://saturnapi.com/