vector space

English - Turkish

Definition of vector space in English Turkish dictionary

(Matematik) doğrusal uzay

vektör uzayı, yöney uzayı, doğrusal uzay

vektör uzayı

yöney uzayı

Related Terms

vector spaces

vektör uzayları

complex vector space

karmaşık doğrusal uzay

left vector space

sol vektör uzayı

ordered vector space

(Matematik) sıralı vektör uzayı

ordered vector space

(Matematik) sıralı yöney uzayı

English - English

Definition of vector space in English English dictionary

A type of set of vectors that satisfies a specific group of constraints

Each vector space has a basis and dimension.

A set V, whose elements are called "vectors", together with a binary operation + forming a module (V,+), and a set F* of bilinear unary functions f*: V→V, each of which corresponds to a "scalar" element f of a field F, such that the composition of elements of F* corresponds isomorphically to multiplication of elements of F, and such that for any vector v, 1*(v) = v

A system consisting of a set of generalized vectors and a field of scalars, having the same rules for vector addition and scalar multiplication as physical vectors and scalars. In mathematics, a collection of objects called vectors, together with a field of objects (see field theory), known as scalars, that satisfy certain properties. The properties that must be satisfied are: (1) the set of vectors is closed under vector addition; (2) multiplication of a vector by a scalar produces a vector in the set; (3) the associative law holds for vector addition, u + (v + w) = (u + v) + w; (4) the commutative law holds for vector addition, u + v = v + u; (5) there is a 0 vector such that v + 0 = v; (6) every vector has an additive inverse (see inverse function), v + (-v) = 0; (7) the distributive law holds for scalar multiplication over vector addition, n(u + v) = nu + nv; (8) the distributive law also holds for vector multiplication over scalar addition, (m + n)v = mv + nv; (9) the associative law holds for scalar multiplication with a vector, (mn)v = m(nv); and (10) there exists a unit vector 1 such that 1v = v. The set of all polynomials in one variable with real coefficients is an example of a vector space

Related Terms

real vector space

A vector space over the field of real numbers.http: //mathworld.wolfram.com/RealVectorSpace.html

Hyphenation

vec·tor space

Turkish pronunciation

vektır speys

Synonyms

linear space

Pronunciation

/ˈvektər ˈspās/ /ˈvɛktɜr ˈspeɪs/