i did a lot of matrix analysis during my grad study, from statistics (general linear model, projection, pseudo inverse, design of experiment, etc) to dynamic system (control, state space, etc) using matlab -- i even used it to generate random distribution from uniform for simulations

the closest thing to matlab is python+numaray+matplotlib (maybe it changes name to scipy?)

i think she will face matrix calculation ... so, use python (matlab is easier, but less flexible) ... i didn't go too far with R but from my experience it's less flexible than python

NB: i did those 5 years ago so don't trust my words too much