Re: A question about Axiom capabilities

> I've been looking for some CAS that provided significant symbolic matrix
> manipulations, including matrix calculus.

Maybe you should look at SymPy. They have some (although limited)
support for symbolic matrix expressions and computations.

SymPy documentation:

 http://docs.sympy.org/0.7.2/modules/matrices/expressions.html
 http://docs.sympy.org/0.7.2/modules/matrices/immutablematrices.html

And various Blog posts:

 http://planet.sympy.org/
 http://matthewrocklin.com/blog/

Hope this helps.