a) A type of set of vectors that satisfies a specific group of constraints.
A vector space is a set of vectors which can be linearly combined.
b) A set V, whose elements are called "vectors", together with a binary operation + forming a module (V,+), and a set F of bilinear unary functions f:V→V, each of which corresponds to a "scalar" element f of a field F, such that the composition of elements of F corresponds isomorphically to multiplication of elements of F, and such that for any vector v, 1(v) = v.
Each vector space has a basis and dimension. vector space over the field F
Syn: linear space
Wikipedia foundation.