In this article, vectors are represented in boldface to distinguish them from scalars.
A vector space over a field F is a non-empty set V together with a binary operation and a binary function that satisfy the eight axioms listed … See more

Vector spaces stem from affine geometry, via the introduction of coordinates in the plane or three-dimensional space. Around 1636, French … See more

The relation of two vector spaces can be expressed by linear map or linear transformation. They are functions that reflect the vector … See more

From the point of view of linear algebra, vector spaces are completely understood insofar as any vector space over a given field is characterized, up to isomorphism, by its dimension. … See more

Linear combination Given a set G of elements of a F-vector space V, a linear combination of elements of G is an element of V of the form See more

Arrows in the plane
The first example of a vector space consists of arrows in a fixed plane, starting at one fixed point. … See more

In addition to the above concrete examples, there are a number of standard linear algebraic constructions that yield vector spaces … See more