I find working with matrices cleaner in MATLAB and the documentation/implementation of higher-level matrix functions more informative (and easier to relate to textbook instruction of Linear Algebra). I have only used MATLAB for the past 3 years, so my experience is limited. Although Livescripts have been a welcome addition to MATLAB, I still prefer Mathematica as a comfortable graphical interactive workspace. I have abused Mathematica since version 3 and right out of the gate I will say that the Notebook interface remains unparalleled compared to other platforms: MATHLAB, Python, R, Stata (of which I have working experience). Or maybe more specific: What can one say to peers (and potential new users) to try and reduce the misconception that Mathematica is solely a symbolic homework solver? Without getting into fanboy arguments of which software is better, what is Mathematica's specific strengths compared to other software, under a 'philosophy of design' standpoint? Is this solely a marketing problem? However, I still don't quite understand the inherent philosophy between the software and Mathematica's exact numeric solving strengths to be able to discuss with MATLAB or Maple users on how Mathematica is just as good as them in its abilities. I've read other mentions in comments around the Stack Exchange sites that Mathematica treats everything as an expression and MATLAB everything a matrix, and both are heavily optimised for this. I am also not old enough to know how Mathematica used to be compared to other software in the same period to know if it wasn't as "good" as it is now. However, I must also admit before I started actually using the software, I've also only really understood it as a symbolic notebook styled software that I knew some people used to do homework with. As a couple year user of Mathematica, I find this a huge misunderstanding in Mathematica's breadth of capabilities. Typically, most people seem to understand Mathematica as a purely symbolic solver, and MATLAB a numeric one, both very strong in their respective fields, but if one wants to do "real" research, Mathematica isn't the software to use. During a typical (possibly with alcohol mixed) discussion among some academic peers in regards to numeric calculation and general modern use of computers in science and engineering settings, it become a heated argument (as it has in many instances in the past) into the comparisons of MATLAB and Mathematica, namely what appears to me, to be a misunderstanding as to what Mathematica really is.or what it really can do.
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