[maximilian]

Matlab is good at prototyping what one might actually build in another language. Its basically a regular python like language that has lots of built-ins for doing stuff with vectors and matrices and plotting things nicely.

Mathematica on the other hand is more of a tool for doing things symbolically (x's & y's). You can integrate, differentiate, find roots, etc all symbolically. It does have tools for doing numerical integrations and such, but they are much more of a black box than matlab's and are very hard to port out of mathematica. Some math folks don't like mathematica because of its black-box attitude, which is understandable. I use it sometimes for calculus.

Don't do linear algebra with mathematica. Matlab is waaay better at it.