Hi,

I've been thinking about GSoC and looking at the various ideas people have been 
posting. By the way, I'd like to see perturbation theory included in general 
(i.e., not just for quantum mechanics) since it's used in stability analysis.

I have a few linear algebra related ideas I'd like to see. One is "abstract" 
linear algebra. That is support for arbitrary matrix and vector calculations. 
So, one would just indicate that a symbol is a matrix/vector without stating 
the size. Then you could work with them. The non-commutative support is a 
start, but the transpose operation would need to be added along with 
derivatives. I have a Maple worksheet that has a crude version of this. This is 
used quite a bit in the Ritz approach to Finite Element Analysis.

The other linear algebra thing to add is support for block matrices. So, one 
could specify a matrix like

M = [[A,B],[C,D]] 

where A, B, C, and D are arbitrary matrices. Then, you could take the inverse 
and other standard linear algebra. This fits in with the "abstract" linear 
algebra support. This kind of thing pops up a lot in control theory.

Cheers,

Tim.

---
Tim Lahey
PhD Candidate, Systems Design Engineering
University of Waterloo
http://about.me/tjlahey


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