Is there a clean way to write a non-uniform scale similar to the format S_a(x) shown for uniform scales?

matrix multiplication?

Outside of matrix multiplication, I mean.

Might depend on what you define as clean, as it could be represented as a piecewise function, or a function per dimension.

True enough. I'm just wondering if there's any formal nomenclature like the format I wrote above for non-uniform scaling. Based on the lack of one in the slide deck, I'm assuming there isn't.

Do you have to position at least one vertex of the polygon at the origin to scale uniformly? I'm confused by the solution of problem 1 in exercise 1