Phrase guide

Hilbert space

noun · 2 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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No pronunciation record was provided for this word.

1

noun

Meaning 1

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

Definition source: English Wiktionary via Wiktextract

Usage: countable, uncountable

Qualifier: functional analysis

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

a metric space that is linear and complete and (usually) infinite-dimensional

Definition source: Princeton WordNet 3.0

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

Broader terms: metric space

History

Etymology

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

Across languages

Translations

21 source translations are retained for this English entry.

  • Afrikaans: Hilbert-ruimte — a space in mathematics
  • Azerbaijani: Hilbert fəzası — a space in mathematics
  • Bulgarian: хилбертово пространство (hilbertovo prostranstvo) — a space in mathematics
  • Chinese Cantonese: 希爾伯特空間 /希尔伯特空间 (hei1 ji5 baak3 dak6 hung1 gaan1) — a space in mathematics
  • Chinese Mandarin: 希爾伯特空間 /希尔伯特空间 (Xī'ěrbótè kōngjiān) — a space in mathematics
  • Danish: Hilbertrum — a space in mathematics
  • Finnish: Hilbertin avaruus — a space in mathematics
  • French: espace de Hilbert — a space in mathematics
  • German: Hilbertraum — a space in mathematics
  • German: Hilbert-Raum — a space in mathematics
  • Hungarian: Hilbert-tér — a space in mathematics
  • Italian: spazio di Hilbert — a space in mathematics
  • Italian: spazio hilbertiano — a space in mathematics
  • Japanese: ヒルベルト空間 (Hiruberuto-kūkan) — a space in mathematics
  • Kazakh: гильберттік кеңістік (gilberttık keñıstık) — a space in mathematics
  • Korean: 힐베르트 공간 (hilbereuteu gonggan) — a space in mathematics
  • Polish: przestrzeń Hilberta — a space in mathematics
  • Portuguese: espaço de Hilbert — a space in mathematics
  • Romanian: spațiu Hilbert — a space in mathematics
  • Russian: ги́льбертово простра́нство (gílʹbertovo prostránstvo) — a space in mathematics
  • Swedish: Hilbertrum — a space in mathematics