The conclusion in #987 is not completely clear, but I have just reread the issue and from [this](https://github.com/JuliaLang/julia/issues/987#issuecomment-31551415) comment I'd say that `AbstractMatrix` is about the same as what you call a linear operator. In particular, subtypes of `AbstractMatrix` don't have to define `size`.

I realise that I lost the vote, so you better come up with some fancy vectors for the `UniformScaling`.