There are several "matrix languages" that support array data and
provide matric inversion as well as solvers, including: Matlab/octave,
IDL/gdl, S+/R. Of these, the S+/R language is the most modern. It is
written by and for statisticians, but offers much the same linear
algebra capabilities found in Matlab/octave and IDL/gdl. If you
aren't already familiar with Matlab or IDL then I recommend R. The
documentation is excellent and it is very widely used.
Whilst I agree with the R recommendation, the 'documentation is
excellent' bit I strongly disagree with. I count on one hand open
source projects with 'excellent' documentation, although this a
subjective subject.
I have recently been introduced to R and forced to learn it after many
years C++, and have found the experience quite (pleasantly) eye-opening,
but not through the documentation - rather through a colleague mentoring me.
R has huge applicability far beyond statistics, yet all the beginner
docs I have read over-stress its (very capable) statistical
functionality and provide only very rough guides to its expressive
abilities and its wide applicability outside of statistics.
It might not sound like it, but this is really a strong vote for R. I
just think the docs are too biased towards to stats, thats all.
FWIW,
Martin
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