In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. It is sometimes...

means that, for two vector spaces over a given field and with the same dimension, the properties that depend only on the vector-space structure are exactly...

is the manifold's dimension. For connected differentiable manifolds, the dimension is also the dimension of the tangent vector space at any point. In geometric...

Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, in Euclid's Elements, it was the three-dimensional space...

finite-dimensional vector spaces. However, many of the principles are also valid for infinite-dimensional vector spaces. A basis B of a vector space V over...

by more specific terms. Any field K {\displaystyle K} is a one-dimensional vector space over itself. The projective line over K , {\displaystyle K,} denoted...

page lists some examples of vector spaces. See vector space for the definitions of terms used on this page. See also: dimension, basis. Notation. Let F denote...

projective space of dimension n is defined as the set of the vector lines (that is, vector subspaces of dimension one) in a vector space V of dimension n + 1...

In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. A norm is a generalization...

The orientation of a real vector space or simply orientation of a vector space is the arbitrary choice of which ordered bases are "positively" oriented...