The term Frob has typically been used to refer to any small device or object (usually hand-sized) which can be manipulated, or frobbed. It was adopted by the community of computer programmers which grew out of the MIT Tech Model Railroad Club in the 1950s. Frob is among the oldest existing words in hacker jargon, as reported in the Jargon File.
The term can refer both to the object being frobbed ("Hand me that frob there, willya?") or as an actual verb ("Hey, frob the switch.") indicating the manipulation of a frob.
Frob is an abbreviation and reference to the well-known "Frobenius Transformation" in algebra (named after Georg Frobenius). The frobenius transform is a similarity transformation used to convert a matrix into rational canonical normal form, which reflects the structure of its minimal polynomial. In this sense, the clearly metaphoric use of the abbreviative word frob (as a verb) evokes the act of making a small perturbative change to a object (or system), in a manner which produces an object that is similar, but posesses a simpler and more rational descriptive structure than the original object, i.e. prior to frobbing. Using frob as a noun is grammatically appropriate only when one is referring to the perturbative action as an object in its own right, though in popular culture these grammatical nuances are no longer observed.