In parallel to the discussion on parameters, I think we should bring up the discussion of linear maps. Not every linear system that is to be solved is a matrix, in many cases one might want to solve with a linear operator or a linear map. Generalizing it like this computationally good because things like matrix-free methods can be much faster and/or take much less memory.
IterativeSolvers.jl seems to want to go this direction by using LinearMaps.jl
I think it would be nice if more packages try to support at least something like linear maps. If I understand correctly, a WrappedMap is just a matrix wrapped as a linear map, so I assume that the package handles the cases to make this work anywhere a matrix \ would work (does it?).
Then the push would really be about trying to get other libraries to support something like the FunctionMap where you define a function for A*x. It’s clear that iterative solvers “can” work with this, but what packages can be made compatible with something like this? Do things like CUSOLVER and PETSc strictly require a matrix?