There was some discussion of this in the sage group. The code will also work 
in SymPy:

http://ask.sagemath.org/question/505/symbolic-matrices
(also see 
http://stackoverflow.com/questions/5708208/symbolic-matrices-in-mathematica-with-unknown-dimensions/5710838
)

This type of approach seems to be what you were talking about, and can 
easily be extended to contain the is_positive_definite type properties.
It needs some work to make inverse work nicely with a square product of 
rectangular matrices, etc...

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