n. a mathematical structure consisting an Abelian group, whose elements are called vectors, and a field, whose elements are called scalars. A further operation, scalar multiplication, is defined, yielding a vector as the 'scalar' product, or just 'product', of a scalar and a vector. This operation distributes over addition of both scalar s and vectors, and is associative with multiplication of scalars; that is
λ(v + w) = λv + λw;
(λ + μ)v = λv + μv;
λ(μv) = (λμ)v.
In analysis, the field is typically the real or complex numbers.