> I would say that your stipulation is (if anything) the wrong way around - most people I know would limit representation theory to linear actions on a vector s

> I would say that your stipulation is (if anything) the wrong way around - most people I know would limit representation theory to linear actions on a vector space (or module over a PID), but would not limit it to a group G: there are groups, Lie algebras, algebras in general, etc etc. That's a very good point about other kinds of 'representers' —though I think it doesn't change the central point that, in some sense, linear algebra seems to focus on "spaces as objects", whereas representation theory, loosely, focuses on "morphisms as objects". I agree that most people will mean when they refer to representations to refer to linear actions, but every so often one does encounter references to, say, actions on sets as 'permutation representations' (although that also has a, closely related, linear-action meaning). I just meant to acknowledge that occasional extra inclusiveness.