I used Mathematica extensively for my physics Ph.D. at Caltech (the same degree and school as Stephen Wolfram---though he finished in two years at the age of 20, instead of six at 29...) I've only used MATLAB sparingly, so I'm can't offer much of a comparison, but Mathematica is excellent at linear algebra: http://reference.wolfram.com/mathematica/guide/MatricesAndLi...