Hilbert space

English

Etymology

Named after German mathematician David Hilbert (1862–1943).

Noun

Hilbert space (countable and uncountable, plural Hilbert spaces)

1. (functional analysis) A generalized Euclidean space in which mathematical functions take the place of points; crucial to the understanding of quantum mechanics and other applications.

Hypernyms

• inner product space

Hyponyms

• Euclidean space
• projective Hilbert space

Derived terms

• isohilbert space
• projective Hilbert space

Related terms

• Banach space
• Fréchet space
• inner product space
• linear algebra
• metric space
• normed space
• pre-Hilbert space
• topological vector space
• vector space

 

Translations

a space in mathematics

• Afrikaans: Hilbert-ruimte
• Azerbaijani: Hilbert fəzası
• Chinese:

  Cantonese: 希爾伯特空間 / 希尔伯特空间 (hei¹ ji⁵ baak³ dak⁶ hung¹ gaan¹)

  Mandarin: 希爾伯特空間 / 希尔伯特空间 (Xī'ěrbótè kōngjiān)

• Danish: Hilbertrum n
• Finnish: Hilbertin avaruus
• French: espace de Hilbert m
• German: Hilbertraum m, Hilbert-Raum
• Hungarian: Hilbert-tér (hu)
• Italian: spazio di Hilbert, spazio hilbertiano
• Japanese: ヒルベルト空間 (ja) (Hiruberuto-kūkan)
• Kazakh: гильберттік кеңістік (gilberttık keñıstık)
• Korean: 힐베르트 공간 (hilbereuteu gonggan)
• Portuguese: espaço de Hilbert m
• Romanian: spațiu Hilbert n
• Russian: ги́льбертово простра́нство n (gílʹbertovo prostránstvo)
• Swedish: Hilbertrum (sv) n

Further reading

• Hilbert space on Wikipedia.Wikipedia