structural:summarization, structural:expansion
Scalars of vector spaces

A vector space is defined as a set of vectors (additive abelian group), a set of scalars (field), and a scalar multiplication operation that takes a scalar k and a vector v to form another vector k v. For example, in a coordinate space, the scalar multiplication k (v 1, v 2, …, v n) {\displaystyle k(v_{1},v_{2},\dots,v_{n})} yields (k v 1, k v 2, …, k v n) {\displaystyle (kv_{1},kv_{2},\dots,kv_{n})}. In a (linear) function space, kf is the function x ↦ k (f (x)).

The scalars can be taken from any field, including the rational, algebraic, real, and complex numbers, as well as finite fields.