In mathematics, convenient vector spaces are locally convex vector spaces satisfying a very mild completeness condition. Traditional differential calculus...

functional analysis, a Banach space (pronounced [ˈbanax]) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows...

(or length) and direction. Euclidean vectors can be added and scaled to form a vector space. A Euclidean vector is frequently represented by a directed...

In mathematics, a set B of vectors in a vector space V is called a basis (pl.: bases) if every element of V may be written in a unique way as a finite...

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase...

Euclidean vector space (named here E {\displaystyle E} ), and is denoted by the symbol × {\displaystyle \times } . Given two linearly independent vectors a and...

Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces...

column space (also called the range or image) of a matrix A is the span (set of all possible linear combinations) of its column vectors. The column space of...

The last three components of a 4–vector must be a standard vector in three-dimensional space. Therefore, a 4–vector must transform like ( c Δ t , Δ x...

transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a representation space of the standard representation...