See Hilbert space in All languages combined, or Wiktionary
Download JSON data for Hilbert space meaning in English (5.5kB)
{
"etymology_templates": [
{
"args": {
"1": "mathematician",
"2": "",
"3": "",
"4": "",
"5": ""
},
"expansion": "mathematician",
"name": "named-after/list"
},
{
"args": {},
"expansion": "|",
"name": "!"
},
{
"args": {
"1": "en",
"2": "David Hilbert"
},
"expansion": "David Hilbert",
"name": "lang"
},
{
"args": {
"1": "en",
"2": "David Hilbert",
"born": "1862",
"died": "1943",
"nat": "German",
"occ": "mathematician",
"wplink": "="
},
"expansion": "Named after German mathematician David Hilbert (1862–1943)",
"name": "named-after"
}
],
"etymology_text": "Named after German mathematician David Hilbert (1862–1943).",
"forms": [
{
"form": "Hilbert spaces",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Hilbert space (plural Hilbert spaces)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "English entries with topic categories using raw markup",
"parents": [
"Entries with topic categories using raw markup",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "English terms with non-redundant non-automated sortkeys",
"parents": [
"Terms with non-redundant non-automated sortkeys",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Functional analysis",
"orig": "en:Functional analysis",
"parents": [
"Mathematical analysis",
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Functions",
"orig": "en:Functions",
"parents": [
"Algebra",
"Calculus",
"Geometry",
"Mathematical analysis",
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"derived": [
{
"word": "isohilbert space"
},
{
"word": "projective Hilbert space"
}
],
"glosses": [
"A generalized Euclidean space in which mathematical functions take the place of points; crucial to the understanding of quantum mechanics and other applications."
],
"hypernyms": [
{
"word": "inner product space"
}
],
"hyponyms": [
{
"word": "Euclidean space"
},
{
"word": "projective Hilbert space"
}
],
"id": "en-Hilbert_space-en-noun-vqJ9ZDRz",
"links": [
[
"functional analysis",
"functional analysis"
],
[
"Euclidean",
"Euclidean#English"
],
[
"mathematical",
"mathematical"
],
[
"functions",
"function#English"
],
[
"points",
"point#English"
],
[
"quantum mechanics",
"quantum mechanics"
]
],
"qualifier": "functional analysis",
"raw_glosses": [
"(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."
],
"related": [
{
"word": "Banach space"
},
{
"word": "Fréchet space"
},
{
"word": "inner product space"
},
{
"word": "linear algebra"
},
{
"word": "metric space"
},
{
"word": "normed space"
},
{
"word": "pre-Hilbert space"
},
{
"word": "topological vector space"
},
{
"word": "vector space"
}
],
"translations": [
{
"code": "af",
"lang": "Afrikaans",
"sense": "a space in mathematics",
"word": "Hilbert-ruimte"
},
{
"code": "az",
"lang": "Azerbaijani",
"sense": "a space in mathematics",
"word": "Hilbert fəzası"
},
{
"code": "yue",
"lang": "Chinese Cantonese",
"sense": "a space in mathematics",
"word": "希爾伯特空間"
},
{
"code": "yue",
"lang": "Chinese Cantonese",
"roman": "hei¹ ji⁵ baak³ dak⁶ hung¹ gaan¹",
"sense": "a space in mathematics",
"word": "希尔伯特空间"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "a space in mathematics",
"word": "希爾伯特空間"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "Xī'ěrbótè kōngjiān",
"sense": "a space in mathematics",
"word": "希尔伯特空间"
},
{
"code": "da",
"lang": "Danish",
"sense": "a space in mathematics",
"tags": [
"neuter"
],
"word": "Hilbertrum"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "a space in mathematics",
"word": "Hilbertin avaruus"
},
{
"code": "fr",
"lang": "French",
"sense": "a space in mathematics",
"tags": [
"masculine"
],
"word": "espace de Hilbert"
},
{
"code": "de",
"lang": "German",
"sense": "a space in mathematics",
"tags": [
"masculine"
],
"word": "Hilbertraum"
},
{
"code": "de",
"lang": "German",
"sense": "a space in mathematics",
"word": "Hilbert-Raum"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "a space in mathematics",
"word": "Hilbert-tér"
},
{
"code": "it",
"lang": "Italian",
"sense": "a space in mathematics",
"word": "spazio di Hilbert"
},
{
"code": "it",
"lang": "Italian",
"sense": "a space in mathematics",
"word": "spazio hilbertiano"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "Hiruberuto-kūkan",
"sense": "a space in mathematics",
"word": "ヒルベルト空間"
},
{
"code": "kk",
"lang": "Kazakh",
"roman": "gilberttık keñıstık",
"sense": "a space in mathematics",
"word": "гильберттік кеңістік"
},
{
"code": "ko",
"lang": "Korean",
"roman": "hilbereuteu gonggan",
"sense": "a space in mathematics",
"word": "힐베르트 공간"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "a space in mathematics",
"tags": [
"masculine"
],
"word": "espaço de Hilbert"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "a space in mathematics",
"tags": [
"neuter"
],
"word": "spațiu Hilbert"
},
{
"code": "ru",
"lang": "Russian",
"roman": "gílʹbertovo prostránstvo",
"sense": "a space in mathematics",
"tags": [
"neuter"
],
"word": "ги́льбертово простра́нство"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "a space in mathematics",
"tags": [
"neuter"
],
"word": "Hilbertrum"
}
],
"wikipedia": [
"Hilbert space"
]
}
],
"word": "Hilbert space"
}
{
"derived": [
{
"word": "isohilbert space"
},
{
"word": "projective Hilbert space"
}
],
"etymology_templates": [
{
"args": {
"1": "mathematician",
"2": "",
"3": "",
"4": "",
"5": ""
},
"expansion": "mathematician",
"name": "named-after/list"
},
{
"args": {},
"expansion": "|",
"name": "!"
},
{
"args": {
"1": "en",
"2": "David Hilbert"
},
"expansion": "David Hilbert",
"name": "lang"
},
{
"args": {
"1": "en",
"2": "David Hilbert",
"born": "1862",
"died": "1943",
"nat": "German",
"occ": "mathematician",
"wplink": "="
},
"expansion": "Named after German mathematician David Hilbert (1862–1943)",
"name": "named-after"
}
],
"etymology_text": "Named after German mathematician David Hilbert (1862–1943).",
"forms": [
{
"form": "Hilbert spaces",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Hilbert space (plural Hilbert spaces)",
"name": "en-noun"
}
],
"hypernyms": [
{
"word": "inner product space"
}
],
"hyponyms": [
{
"word": "Euclidean space"
},
{
"word": "projective Hilbert space"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "Banach space"
},
{
"word": "Fréchet space"
},
{
"word": "inner product space"
},
{
"word": "linear algebra"
},
{
"word": "metric space"
},
{
"word": "normed space"
},
{
"word": "pre-Hilbert space"
},
{
"word": "topological vector space"
},
{
"word": "vector space"
}
],
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English entries with topic categories using raw markup",
"English eponyms",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with non-redundant non-automated sortkeys",
"en:Functional analysis",
"en:Functions"
],
"glosses": [
"A generalized Euclidean space in which mathematical functions take the place of points; crucial to the understanding of quantum mechanics and other applications."
],
"links": [
[
"functional analysis",
"functional analysis"
],
[
"Euclidean",
"Euclidean#English"
],
[
"mathematical",
"mathematical"
],
[
"functions",
"function#English"
],
[
"points",
"point#English"
],
[
"quantum mechanics",
"quantum mechanics"
]
],
"qualifier": "functional analysis",
"raw_glosses": [
"(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."
],
"wikipedia": [
"Hilbert space"
]
}
],
"translations": [
{
"code": "af",
"lang": "Afrikaans",
"sense": "a space in mathematics",
"word": "Hilbert-ruimte"
},
{
"code": "az",
"lang": "Azerbaijani",
"sense": "a space in mathematics",
"word": "Hilbert fəzası"
},
{
"code": "yue",
"lang": "Chinese Cantonese",
"sense": "a space in mathematics",
"word": "希爾伯特空間"
},
{
"code": "yue",
"lang": "Chinese Cantonese",
"roman": "hei¹ ji⁵ baak³ dak⁶ hung¹ gaan¹",
"sense": "a space in mathematics",
"word": "希尔伯特空间"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "a space in mathematics",
"word": "希爾伯特空間"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "Xī'ěrbótè kōngjiān",
"sense": "a space in mathematics",
"word": "希尔伯特空间"
},
{
"code": "da",
"lang": "Danish",
"sense": "a space in mathematics",
"tags": [
"neuter"
],
"word": "Hilbertrum"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "a space in mathematics",
"word": "Hilbertin avaruus"
},
{
"code": "fr",
"lang": "French",
"sense": "a space in mathematics",
"tags": [
"masculine"
],
"word": "espace de Hilbert"
},
{
"code": "de",
"lang": "German",
"sense": "a space in mathematics",
"tags": [
"masculine"
],
"word": "Hilbertraum"
},
{
"code": "de",
"lang": "German",
"sense": "a space in mathematics",
"word": "Hilbert-Raum"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "a space in mathematics",
"word": "Hilbert-tér"
},
{
"code": "it",
"lang": "Italian",
"sense": "a space in mathematics",
"word": "spazio di Hilbert"
},
{
"code": "it",
"lang": "Italian",
"sense": "a space in mathematics",
"word": "spazio hilbertiano"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "Hiruberuto-kūkan",
"sense": "a space in mathematics",
"word": "ヒルベルト空間"
},
{
"code": "kk",
"lang": "Kazakh",
"roman": "gilberttık keñıstık",
"sense": "a space in mathematics",
"word": "гильберттік кеңістік"
},
{
"code": "ko",
"lang": "Korean",
"roman": "hilbereuteu gonggan",
"sense": "a space in mathematics",
"word": "힐베르트 공간"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "a space in mathematics",
"tags": [
"masculine"
],
"word": "espaço de Hilbert"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "a space in mathematics",
"tags": [
"neuter"
],
"word": "spațiu Hilbert"
},
{
"code": "ru",
"lang": "Russian",
"roman": "gílʹbertovo prostránstvo",
"sense": "a space in mathematics",
"tags": [
"neuter"
],
"word": "ги́льбертово простра́нство"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "a space in mathematics",
"tags": [
"neuter"
],
"word": "Hilbertrum"
}
],
"word": "Hilbert space"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.