Well, we're about 1/2-way done now. I guess I'm pretty happy with both my contribution and what I've learned (coding-wise). I think the matrix manipulation functionality is pretty high now, there's an inverter, a different solver, some factorization methods and some other stuff. I guess some of today will be spent filling out this survey.
I guess my next step will be to try and flush out the expression evaluation problem. Then add a bit more new eigenvalue-related functionality. I've been in touch with Robert who has help me out by writing a wrapper for me to use for solving for eigenvalues. Thanks Robert!
After that, who knows? I'm considering adding more matrix types (e.g. integer) with more optimized algorithms behind the scenes but I'll cross that bridge after the eigenvalue dance.