Hilbert–Schmidt operator

en

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Hilbert–Schmidt operator

Quality:

Hilbert–Schmidt operator - nuclear operator of order 2; a bounded operator A on a Hilbert space H such that tr(A*A) is finite. Article "Hilbert–Schmidt operator" in English Wikipedia has 32.2 points for quality (as of July 1, 2025). The article contains 18 references and 6 sections.

In this language version of Wikipedia the article has the best quality. Also, this article is the most popular in that language version.

Since the creation of article "Hilbert–Schmidt operator", its content was written by 46 registered users of English Wikipedia and edited by 108 registered Wikipedia users in all languages.

The article is cited 493 times in English Wikipedia and cited 742 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #118986 in September 2005
  • Global: #134169 in January 2012

The highest popularity rank from 2008:

  • Local (English): #317453 in November 2022
  • Global: #455097 in November 2022

There are 8 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

Languages with the highest quality

#LanguageQuality gradeQuality score
1English (en)
Hilbert–Schmidt operator
32.154
2Ukrainian (uk)
Оператор Гільберта — Шмідта
22.4928
3Chinese (zh)
希尔伯特-施密特算子
12.0354
4Italian (it)
Operatore di Hilbert-Schmidt
11.1596
5German (de)
Hilbert-Schmidt-Operator
8.8068
6Russian (ru)
Оператор Гильберта — Шмидта
6.8352
7Japanese (ja)
ヒルベルト=シュミット作用素
6.1436
8Polish (pl)
Operator Hilberta-Schmidta
4.1142
More...

The following table shows the most popular language versions of the article.

Most popular in all the time

The most popular language versions of the article "Hilbert–Schmidt operator" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Hilbert–Schmidt operator
398 909
2German (de)
Hilbert-Schmidt-Operator
66 386
3Russian (ru)
Оператор Гильберта — Шмидта
22 342
4Japanese (ja)
ヒルベルト=シュミット作用素
18 874
5Italian (it)
Operatore di Hilbert-Schmidt
12 513
6Chinese (zh)
希尔伯特-施密特算子
10 729
7Polish (pl)
Operator Hilberta-Schmidta
7 742
8Ukrainian (uk)
Оператор Гільберта — Шмідта
311
More...

The following table shows the language versions of the article with the highest popularity in the last month.

Most popular in June 2025

The most popular language versions of the article "Hilbert–Schmidt operator" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Hilbert–Schmidt operator
2 778
2German (de)
Hilbert-Schmidt-Operator
266
3Japanese (ja)
ヒルベルト=シュミット作用素
149
4Chinese (zh)
希尔伯特-施密特算子
110
5Italian (it)
Operatore di Hilbert-Schmidt
89
6Russian (ru)
Оператор Гильберта — Шмидта
76
7Polish (pl)
Operator Hilberta-Schmidta
22
8Ukrainian (uk)
Оператор Гільберта — Шмідта
10
More...

The following table shows the language versions of the article with the highest Authors’ Interest.

The highest AI

Language versions of the article "Hilbert–Schmidt operator" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Hilbert–Schmidt operator
46
2German (de)
Hilbert-Schmidt-Operator
17
3Russian (ru)
Оператор Гильберта — Шмидта
15
4Italian (it)
Operatore di Hilbert-Schmidt
12
5Japanese (ja)
ヒルベルト=シュミット作用素
7
6Polish (pl)
Operator Hilberta-Schmidta
6
7Chinese (zh)
希尔伯特-施密特算子
3
8Ukrainian (uk)
Оператор Гільберта — Шмідта
2
More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

The highest AI in June 2025

Language versions of the article "Hilbert–Schmidt operator" with the highest AI in June 2025
#LanguageAI awardRelative AI
1German (de)
Hilbert-Schmidt-Operator
0
2English (en)
Hilbert–Schmidt operator
0
3Italian (it)
Operatore di Hilbert-Schmidt
0
4Japanese (ja)
ヒルベルト=シュミット作用素
0
5Polish (pl)
Operator Hilberta-Schmidta
0
6Russian (ru)
Оператор Гильберта — Шмидта
0
7Ukrainian (uk)
Оператор Гільберта — Шмідта
0
8Chinese (zh)
希尔伯特-施密特算子
0
More...

The following table shows the language versions of the article with the highest number of citations.

The highest CI

Language versions of the article "Hilbert–Schmidt operator" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Hilbert–Schmidt operator
493
2Chinese (zh)
希尔伯特-施密特算子
91
3Japanese (ja)
ヒルベルト=シュミット作用素
56
4German (de)
Hilbert-Schmidt-Operator
34
5Ukrainian (uk)
Оператор Гільберта — Шмідта
34
6Russian (ru)
Оператор Гильберта — Шмидта
23
7Italian (it)
Operatore di Hilbert-Schmidt
6
8Polish (pl)
Operator Hilberta-Schmidta
5
More...

Scores

Estimated value for Wikipedia:
English:
Global:
Popularity in June 2025:
English:
Global:
Popularity in all years:
English:
Global:
Authors in June 2025:
English:
Global:
Registered authors in all years:
English:
Global:
Citations:
English:
Global:

Quality measures

Interwikis

#LanguageValue
deGerman
Hilbert-Schmidt-Operator
enEnglish
Hilbert–Schmidt operator
itItalian
Operatore di Hilbert-Schmidt
jaJapanese
ヒルベルト=シュミット作用素
plPolish
Operator Hilberta-Schmidta
ruRussian
Оператор Гильберта — Шмидта
ukUkrainian
Оператор Гільберта — Шмідта
zhChinese
希尔伯特-施密特算子

Popularity rank trends

Best Rank English:
#317453
11.2022
Global:
#455097
11.2022

AI rank trends

Best Rank English:
#118986
09.2005
Global:
#134169
01.2012

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Hilbert–Schmidt operator from Wikipedia articles about Matrix norm, Frobenius inner product, Hilbert–Schmidt integral operator, Trace class operator and Schatten norm. Whereas reading the article about Hilbert–Schmidt operator people most often go to Wikipedia articles on Matrix norm, Trace class operator, Hilbert–Schmidt integral operator, Frobenius inner product and Sazonovs theorem.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

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About WikiRank

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information