Is Mathematica as good as Matlab for linear algebra?
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.
for linear algebra, matlab is more succinct, it has "'" transpose and "^-1" for inverse, so you can type x = A'(AA')^-1*b
Mathematica has an extensive set of typesetting shortcuts. You just need to know where to look.