TITLE: What is characteristic (function, polynomial, etc)?
QUESTION [6 upvotes]: My question is - what's the nature of characteristic functions, equations and so on? Am I right in understanding that this is just the general term for naming "ways" to find some invariants of some object? Or is there some other meaning?

REPLY [2 votes]: There's no particular reason that mathematicians decide or don't decide to name a property of something a "characteristic ____". The definition of a  "characteristic ____" should be an important definition, I guess, but then again any definition really ought to be important, otherwise it's questionable whether we should be making it. But my point is simply that "characteristic" is just a nice word that might be evocative of a sense you want to attach to the definition in question, and there's no special explicit meaning that ties together its various occurrences (characteristic function, characteristic polynomial, characteristic of a field, etc.).