In mathematics, convenient vector spaces are locally convex vector spaces satisfying a very mild completeness condition. Traditional differential calculus...
20 KB (4,008 words) - 04:50, 15 November 2023
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...
103 KB (17,214 words) - 08:06, 6 March 2024
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...
17 KB (1,836 words) - 18:42, 25 May 2024
(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...
60 KB (9,031 words) - 10:47, 16 April 2024
Basis (linear algebra) (redirect from Linear Algebra/Basis for a Vector Space)
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...
34 KB (4,730 words) - 00:00, 25 September 2023
Cross product (redirect from Vector product)
Euclidean vector space (named here E {\displaystyle E} ), and is denoted by the symbol × {\displaystyle \times } . Given two linearly independent vectors a and...
75 KB (11,464 words) - 04:10, 14 April 2024
Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional) Euclidean vector spaces...
128 KB (17,476 words) - 16:39, 21 April 2024
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...
25 KB (3,682 words) - 16:25, 24 October 2023
transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a representation space of the standard representation...
46 KB (8,249 words) - 23:27, 16 February 2024
Spacetime (redirect from Space-time interval)
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...
198 KB (27,821 words) - 09:34, 9 June 2024