Hilbert space

English

Etymology

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

Noun

Hilbert space (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

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

Translations

a space in mathematics

• Afrikaans: Hilbert-ruimte
• Danish: Hilbertrum n
• Finnish: Hilbertin avaruus
• French: espace de Hilbert m
• German: Hilbertraum m, Hilbert-Raum
• Hungarian: Hilbert-tér (hu)
• (deprecated template usage) {{trans-mid}}
• Italian: spazio di Hilbert, spazio hilbertiano
• Japanese: ヒルベルト空間 (Hiruberuto-kūkan)
• Portuguese: espaço de Hilbert m
• Russian: ги́льбертово простра́нство n (gílʹbertovo prostránstvo)
• Swedish: Hilbertrum (sv) n

Further reading

• Hilbert space on Wikipedia.Wikipedia