English
Noun
wikipedia
vector space
- maths A type of set of vectors that satisfies a specific group of constraints.
#: A vector space is a set of vectors which can be linear combination|linearly combined.
vector space over the field F
- linear algebra A set V, whose elements are called "vectors", together with a binary operation + forming a module (V,+), and a set F<sup>*</sup> of bilinear unary functions f<sup>*</sup>:V→V, each of which corresponds to a "scalar" element f of a field F, such that the composition of elements of F<sup>*</sup> corresponds isomorphically to multiplication of elements of F, and such that for any vector v, 1<sup>*</sup>(v) = v.
#* Any field <math>\mathbb{F}</math> is a one-dimensional vector space over itself.
#* If <math>\mathbb{V}</math> is a vector space over <math>\mathbb{F}</math> and S is any set, then <math>\mathbb{V}^S\{f|f:S\rightarrow \mathbb{V} \}</math> is a vector space over <math>\mathbb{F}</math>, and <math> \mbox{dim} ( \mathbb{V}^S ) \mbox{card}(S) \, \mbox{dim} (\mathbb{V})</math>.
#* If <math>\mathbb{V}</math> is a vector space over <math>\mathbb{F}</math> then any closed subset of <math>\mathbb{V}</math> is also a vector space over <math>\mathbb{F}</math>.
#* The above three rules suffice to construct all vector spaces.
Synonyms
linear space
Translations
Croatian: t-|hr|vektorski prostor|m
Czech: vektorový prostor m
Hungarian: vektortér
Italian: spazio vettoriale m
Swedish: vektorrum n
Category:Algebra
Category:Analysis
Category:Geometry
Category:Linear algebra
Category:Topology
sv:vector space
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