コーシー=シュワルツの不等式

ja

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コーシー=シュワルツの不等式

Quality:

Cauchy–Schwarz inequality - a useful inequality encountered in many different settings, such as linear algebra, analysis, probability theory, vector algebra and other areas. It is considered to be one of the most important inequalities in all of mathematics. Article "コーシー=シュワルツの不等式" in Japanese Wikipedia has 7.4 points for quality (as of November 1, 2023). The article contains 0 references and 9 sections. The article also contains quality flaw template, which reduce quality score.

This article has the best quality in Slovenian Wikipedia. However, the most popular language version of this article is English.

In October 2023 the article "コーシー=シュワルツの不等式" was edited by 1 authors in Japanese Wikipedia and written by 6 authors in all languages.

Since the creation of article "コーシー=シュワルツの不等式", its content was written by 37 registered users of Japanese Wikipedia and edited by 1185 registered Wikipedia users in all languages.

The article is cited 197 times in Japanese Wikipedia and cited 1492 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (Japanese): #1465 in May 2019
  • Global: #429 in August 2001

The highest popularity rank from 2008:

  • Local (Japanese): #40063 in June 2021
  • Global: #16889 in October 2018

There are 39 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 November 1, 2023 (including revision history and pageviews for previous years).

下表顯示了最高品質的文章的語言版本。

Languages with the highest quality

#LanguageQuality gradeQuality score
1Slovenian (sl)
Cauchy–Schwarzova neenakost
52.6483
2English (en)
Cauchy–Schwarz inequality
51.2153
3Greek (el)
Ανισότητα Κωσύ-Σβαρτς
42.6303
4Serbian (sr)
Коши-Шварцова неједнакост
35.2352
5Indonesian (id)
Pertidaksamaan Cauchy–Schwarz
27.9688
6French (fr)
Inégalité de Cauchy-Schwarz
27.6801
7Thai (th)
อสมการโคชี-ชวาร์ซ
25.705
8German (de)
Cauchy-Schwarzsche Ungleichung
24.317
9Chinese (zh)
柯西-施瓦茨不等式
23.9356
10Korean (ko)
코시-슈바르츠 부등식
22.618
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 "コーシー=シュワルツの不等式" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Cauchy–Schwarz inequality
5 082 417
2French (fr)
Inégalité de Cauchy-Schwarz
979 567
3German (de)
Cauchy-Schwarzsche Ungleichung
889 422
4Vietnamese (vi)
Bất đẳng thức Cauchy–Schwarz
727 342
5Chinese (zh)
柯西-施瓦茨不等式
622 804
6Russian (ru)
Неравенство Коши — Буняковского
595 647
7Japanese (ja)
コーシー=シュワルツの不等式
554 476
8Spanish (es)
Desigualdad de Cauchy-Bunyakovsky-Schwarz
402 849
9Korean (ko)
코시-슈바르츠 부등식
354 224
10Italian (it)
Disuguaglianza di Cauchy-Schwarz
346 600
More...

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

Most popular in October 2023

The most popular language versions of the article "コーシー=シュワルツの不等式" in October 2023
#LanguagePopularity awardRelative popularity
1English (en)
Cauchy–Schwarz inequality
52 736
2French (fr)
Inégalité de Cauchy-Schwarz
8 009
3Chinese (zh)
柯西-施瓦茨不等式
7 082
4German (de)
Cauchy-Schwarzsche Ungleichung
5 043
5Russian (ru)
Неравенство Коши — Буняковского
4 016
6Japanese (ja)
コーシー=シュワルツの不等式
2 553
7Italian (it)
Disuguaglianza di Cauchy-Schwarz
2 428
8Spanish (es)
Desigualdad de Cauchy-Bunyakovsky-Schwarz
2 224
9Korean (ko)
코시-슈바르츠 부등식
1 837
10Vietnamese (vi)
Bất đẳng thức Cauchy–Schwarz
1 667
More...

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

The highest AI

Language versions of the article "コーシー=シュワルツの不等式" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Cauchy–Schwarz inequality
279
2German (de)
Cauchy-Schwarzsche Ungleichung
98
3French (fr)
Inégalité de Cauchy-Schwarz
95
4Vietnamese (vi)
Bất đẳng thức Cauchy–Schwarz
76
5Russian (ru)
Неравенство Коши — Буняковского
60
6Italian (it)
Disuguaglianza di Cauchy-Schwarz
49
7Dutch (nl)
Ongelijkheid van Cauchy-Schwarz
41
8Chinese (zh)
柯西-施瓦茨不等式
41
9Norwegian (no)
Cauchy–Schwarz’ ulikhet
40
10Hungarian (hu)
Cauchy–Bunyakovszkij–Schwarz-egyenlőtlenség
39
More...

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

The highest AI in October 2023

Language versions of the article "コーシー=シュワルツの不等式" with the highest AI in October 2023
#LanguageAI awardRelative AI
1English (en)
Cauchy–Schwarz inequality
2
2Hungarian (hu)
Cauchy–Bunyakovszkij–Schwarz-egyenlőtlenség
1
3Japanese (ja)
コーシー=シュワルツの不等式
1
4Slovak (sk)
Cauchyho-Schwarzova nerovnosť
1
5Vietnamese (vi)
Bất đẳng thức Cauchy–Schwarz
1
6Arabic (ar)
متباينة كوشي-شفارتس
0
7Belarusian (be)
Няроўнасць Кашы — Бунякоўскага
0
8Catalan (ca)
Desigualtat de Cauchy-Schwarz
0
9Czech (cs)
Cauchyho–Schwarzova nerovnost
0
10Danish (da)
Cauchy-Schwarz' ulighed
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 "コーシー=シュワルツの不等式" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Cauchy–Schwarz inequality
296
2Japanese (ja)
コーシー=シュワルツの不等式
197
3Italian (it)
Disuguaglianza di Cauchy-Schwarz
157
4Chinese (zh)
柯西-施瓦茨不等式
106
5French (fr)
Inégalité de Cauchy-Schwarz
99
6Hebrew (he)
אי-שוויון קושי-שוורץ
82
7German (de)
Cauchy-Schwarzsche Ungleichung
73
8Ukrainian (uk)
Нерівність Коші — Буняковського
43
9Korean (ko)
코시-슈바르츠 부등식
41
10Russian (ru)
Неравенство Коши — Буняковского
39
More...

Scores

Estimated value for Wikipedia:
Japanese:
Global:
Popularity in October 2023:
Japanese:
Global:
Popularity in all years:
Japanese:
Global:
Authors in October 2023:
Japanese:
Global:
Registered authors in all years:
Japanese:
Global:
Citations:
Japanese:
Global:

Quality measures

Interwikis

#LanguageValue
arArabic
متباينة كوشي-شفارتس
beBelarusian
Няроўнасць Кашы — Бунякоўскага
caCatalan
Desigualtat de Cauchy-Schwarz
csCzech
Cauchyho–Schwarzova nerovnost
daDanish
Cauchy-Schwarz' ulighed
deGerman
Cauchy-Schwarzsche Ungleichung
elGreek
Ανισότητα Κωσύ-Σβαρτς
enEnglish
Cauchy–Schwarz inequality
esSpanish
Desigualdad de Cauchy-Bunyakovsky-Schwarz
etEstonian
Cauchy-Schwarzi võrratus
euBasque
Cauchy-Bunyakovsky-Schwarz-en desberdintza
faPersian
نابرابری کوشی–شوارتز
fiFinnish
Cauchyn–Schwarzin epäyhtälö
frFrench
Inégalité de Cauchy-Schwarz
heHebrew
אי-שוויון קושי-שוורץ
huHungarian
Cauchy–Bunyakovszkij–Schwarz-egyenlőtlenség
idIndonesian
Pertidaksamaan Cauchy–Schwarz
itItalian
Disuguaglianza di Cauchy-Schwarz
jaJapanese
コーシー=シュワルツの不等式
kkKazakh
Коши-Буняковский теңсіздігі
koKorean
코시-슈바르츠 부등식
ltLithuanian
Koši - Švarco nelygybė
nlDutch
Ongelijkheid van Cauchy-Schwarz
noNorwegian
Cauchy–Schwarz’ ulikhet
plPolish
Nierówność Cauchy’ego-Schwarza
ptPortuguese
Desigualdade de Cauchy-Schwarz
roRomanian
Inegalitatea Cauchy-Schwarz
ruRussian
Неравенство Коши — Буняковского
skSlovak
Cauchyho-Schwarzova nerovnosť
slSlovenian
Cauchy–Schwarzova neenakost
srSerbian
Коши-Шварцова неједнакост
svSwedish
Cauchy–Schwarz olikhet
thThai
อสมการโคชี-ชวาร์ซ
trTurkish
Cauchy-Schwarz eşitsizliği
ukUkrainian
Нерівність Коші — Буняковського
urUrdu
کاشی شوارز نامساوات
uzUzbek
Cauchy–Schwarz tengsizligi
viVietnamese
Bất đẳng thức Cauchy–Schwarz
zhChinese
柯西-施瓦茨不等式

Popularity rank trends

Best Rank Japanese:
#40063
06.2021
Global:
#16889
10.2018

AI rank trends

Best Rank Japanese:
#1465
05.2019
Global:
#429
08.2001

Local AI rank history

Global AI rank history

Languages comparison

Important global interconnections

Wikipedia readers most often find their way to information on Cauchy–Schwarz inequality from Wikipedia articles about Triangle inequality, Hölders inequality, Wikipedia article, Scalar product and Minkowski inequality. Whereas reading the article about Cauchy–Schwarz inequality people most often go to Wikipedia articles on Hölders inequality, Inner product space, Hermann Schwarz, Augustin-Louis Cauchy and Triangle inequality.

Cumulative results of quality and popularity of the Wikipedia article

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

News from 6 May 2024

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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 November, 2023. When calculating current popularity and AI of articles data from October 2023 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2023... More information