vector space
A set of elements called vectors, together with some field and operations called…A set of elements called vectors, together with some field and operations called addition (mapping two vectors to a vector) and scalar multiplication (mapping a vector and an element in the field to a vector), satisfying a list of constraints; equivalently, a module over a field.
» These matrices form a vector space.
Ці матриці утворюють векторний простір. — Leonid
Leonid · Tatoeba · CC BY 2.0 FRMeaning
1 sensesA set of elements called vectors, together with some field and operations called addition (mapping two vectors to a vector) and scalar multiplication (mapping a vector and an element in the field to a vector), satisfying a list of constraints; equivalently, a module over a field.
A vector space is a set of vectors which can be linearly combined.
Each vector space has a basis and dimension.
Vektorraum
ве́кторное простра́нствоvéktornoje prostránstvo
векторний простірvektornyj prostir
Examples
7 sentencesThese matrices form a vector space.
Ці матриці утворюють векторний простір. — Leonid
Every vector space has a basis.
deJeder Vektorraum hat eine Basis. — Pfirsichbaeumchen
In mathematics, an algebra over a field is a vector space equipped with a bilinear product.
The dimension of a vector space equals the largest number of its elements that can be linearly independent.
deDie Dimension eines Vektorraums ist gleich der maximalen Anzahl in ihm linear unabhängiger Elemente. — Pfirsichbaeumchen
"Actually, I understood everything in linear algebra until we came to vector spaces," said Tom. Mary just shook her head.
de„Ich habe in der Linearen Algebra eigentlich alles verstanden, bis wir dann zu den Vektorräumen kamen“, meinte Tom. Maria schüttelte nur mit dem Kopf. — Pfirsichbaeumchen
Translations
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Forms
plural: vector spaces| Singular | vector space |
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