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