vector space

English

Pronunciation

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Noun

vector space (plural vector spaces)

1. (algebra, geometry, topology) 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.

   A vector space is a set of vectors which can be linearly combined.

   Each vector space has a basis and dimension.

Synonyms

• linear space

Hypernyms

• module
• free module

Hyponyms

• algebra over a field
• Banach space
• Euclidean space
• inner product space
• normed vector space
• quadratic space
• real vector space

Meronyms

• linear subspace
• subspace
• vector

Translations

mathematics

• Afrikaans: vektorruimte
• Armenian: վեկտորական տարածություն (vektorakan taracutʻyun)
• Asturian: espaciu vectorial m
• Azerbaijani: vektor fəzası
• Basque: bektore espazio
• Belarusian: вектарная прастора f (vjektarnaja prastóra)
• Catalan: espai vectorial m
• Chinese:

  Mandarin: 向量空間 / 向量空间 (xiàngliàng kōngjiān), 矢量空間 / 矢量空间 (shǐliàng kōngjiān)

• Czech: vektorový prostor m
• Danish: vektorrum n
• Dutch: vectorruimte (nl) f
• Esperanto: vektora spaco
• Estonian: vektorruum
• Finnish: vektoriavaruus (fi)
• French: espace vectoriel (fr) m
• Galician: espazo vectorial m
• German: Vektorraum m
• Greek: διανυσματικός χώρος m (dianysmatikós chóros)
• Hungarian: vektortér (hu)
• Icelandic: vigurrúm n
• Indonesian: ruang vektor
• Interlingua: spatio vectorial
• Irish: spás veicteoireach m
• Italian: spazio vettoriale (it) m
• Japanese: ベクトル空間 (ja) (bekutoru kūkan)
• Korean: 벡터 공간 (bekteo gonggan)
• Kyrgyz: вектордук мейкиндик (vektorduk meykindik)
• Lithuanian: vektorinė erdvė f
• Macedonian: векторски простор m (vektorski prostor)
• Malay: ruang vektor
• Malayalam: സദിശസമഷ്ടി (sadiśasamaṣṭi)
• Norwegian: vektorrom (no) n
• Persian: فضای برداری
• Polish: przestrzeń wektorowa f, przestrzeń liniowa f
• Portuguese: espaço vetorial (pt) m
• Romanian: spațiu vectorial n
• Russian: ве́кторное простра́нство (ru) n (véktornoje prostránstvo)
• Serbo-Croatian: vektorski prostor m
• Slovak: vektorový priestor m
• Slovene: vektorski prostor m
• Spanish: espacio vectorial (es) m
• Swedish: vektorrum (sv) n
• Tagalog: espasyong bektor
• Tamil: திசையன் வெளி (ticaiyaṉ veḷi)
• Thai: ปริภูมิเวกเตอร์, ปริภูมิเชิงเส้น
• Turkish: vektör uzayı
• Ukrainian: векторний простір m (vektornyj prostir)
• Vietnamese: không gian vectơ (vi)