Mathematica or Maple?

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Why not MathCAD? It's the most user friendly and does everything you'll want to do. Probably.

I love the tutorials in Maple. And Maple's help/guide is excellent.

Mathematica is good, but expensive.

Matlab? Are you kidding me? Never. Although, having said that I've used Matlab more than all the others combined for linear algebra and control engineering.



as it's between Mathematica & Maple I would go for Maple, because there's really not much between them, but Maple has great tutorials. Although last time I used mathematica was over a year ago and things may have changed significantly since then.

Ah MatLab how I remember that one well especially for electrical engineering (signal processing, optical sensing + imaging). Matrices are what it is designed to do so if linear algebra is what you are pursuing then that can help. However, it is up to you which tool you wish to use. I have used Mathematica & it didn't sit well with me but that being said Octave or Maxima could also work for you however, I haven't personally used those tools.