Can Mathematica do or be modified to do symbolic linear algebra?
for example, I would like it if it could automaticly simplify something like
A^-1 - (A^-1 u v^T A^-1)/(1 + v^T A^-1 u)
to (by Sherman Morrisson)
(A + u v^T)^-1
(I know I am not using Mathematica syntax, but I think you can see what I meen)