vector space
noun1
Algebra, Geometry, Mathematics, Sciences, Topology 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.
- A vector space is a set of vectors which can be linearly combined.
- Each vector space has a basis and dimension.
- Synonyms
- linear space
- Hypernyms
- module, free module
- Hyponyms
- algebra over a field, Banach space, Euclidean space, inner product space, normed vector space, quadratic space, real vector space
- Meronyms
- linear subspace, subspace, vector