Generic API to reconstruct from factorize

Is there a generic function/API to recover the original matrix from a factorization? Eg LinearAlgebra defines Matrix in various places, so

A = randn(5, 5)
F = factorize(A)
Matrix(F) # <- is there a generic API here?

works but this fails for generic <:AbstractArray, eg StaticArrays.SMatrix which has its own LU.

Unfortunately, I think it comes down to this line defining a method specifically on LU. It would be nice if instead factorizations had a method specific for this like

parent(F::LU) = (F.L * F.U)[invperm(F.p),:]

so that it wasn’t necessary to define a bunch of array specific conversions for each factorization.

I realized that simply documenting that an AbstractMatrix method (which currently exists) should be defined for all results of factorize would fix this issue for me.

@andreasnoack, what do you think about this?