vector space — English Dictionary

Noun

1. A set of elements called vectors, together with some field and operations called addition (mapping two vectors to a vector) and scalar multiplication (mapping a vector and an element in the field to a vector), satisfying a list of constraints; equivalently, a module over a field.

   Synonyms

   linear space

   Broader terms

   modulefree module

   Narrower terms

   algebra over a fieldBanach spaceEuclidean spaceinner product spacenormed vector spacequadratic spacereal vector space

   Examples

   A vector space is a set of vectors which can be linearly combined.

   Each vector space has a basis and dimension.