representation

The thing that does the standing-in: a carved figure like the Venus of Willendorf, a painted funeral hatchment bearing a family's arms, or the images of Winnie the Pooh that Chinese censors chase down. The word came through Late Middle English representacioun and Old French from Latin repraesentātiō. It counts naturally (two other representations of the arms), and it usually takes of before whatever is represented.

Here the word names the doing rather than the thing done. The act can be depiction, but it can also be acting for someone. A company unhappy with your representation of it at trade events is objecting to how you spoke for it. The finished object belongs to the "something that stands for" meaning. If you can swap in "the act of" or "the way of," you are here.

Politics folds two things into one word: the right to choose someone who speaks for you, and the seat that person then fills. It usually takes in before the body (representation in the British parliament). Its absence can be a grievance large enough to help drive a revolution, as it did for the American colonists. It is often weighed as a quantity, as when a district's representation is too small.

An extension of depiction into the question of who appears in media and how they are shown. It is uncountable in this use: a film has good or poor representation, never "a representation." Both frequency and treatment matter. The word can praise the care of a portrayal as readily as it measures how often a group appears at all.

Law uses the word collectively, for the whole team acting for a client, so it usually stands without an article. A defendant appears without representation, and people who cannot afford representation may get government help. Legal representation is the common pairing. Unlike the elected voice in government, nobody votes for it. It is hired, or provided when a client cannot pay.

A mathematician's way of turning abstract algebra into linear algebra. Each element of a group or Lie algebra acts on a vector space as a linear map. Once a basis is chosen, each element becomes a matrix, and combining elements becomes multiplying matrices. A representation is faithful when no two elements act alike. It is irreducible when no proper nonzero subspace is preserved by every element. Often the vector space itself is called the representation.

A different word that happens to share the spelling. It is built from re- plus presentation, on the clinician's use of present: a patient presents with symptoms, then comes back as a representation. It usually takes to before the place (representation to the emergency department) and often appears in rates and counts. Nothing but the letters links it to the "standing for" meaning.