Linear algebra/Talk

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So what other stuff has the structure of a linear space but has elements that are not real or complex numbers?

In computational number theory you sometimes get people doing linear algebra on matrices made out of integers modulo a prime. Often the prime is 2, but larger ones are also used.

My guess is the elements have to be from a ring or maybe a field. Anyway something with a group operation on the whole set, another group operation on the set except for identity of the first group, distributive law between the two group operations.

Anything to do with finite fields? --Damian Yerrick