コーシー=シュワルツの不等式

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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 July 1, 2025). The article contains 0 references and 9 sections. The article also contains templates indicating quality issues, therefore its score was reduced by 0.39 points.

This article has the best quality in English Wikipedia. Also, this article is the most popular in that (Japanese) language version.

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 1268 registered Wikipedia users in all languages.

The article is cited 201 times in Japanese Wikipedia and cited 1612 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (Japanese): #1467 in May 2019
  • Global: #490 in August 2001

The highest popularity rank from 2008:

  • Local (Japanese): #40039 in June 2021
  • Global: #16804 in October 2021

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 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)
Cauchy–Schwarz inequality
51.6974
2Slovenian (sl)
Cauchy–Schwarzova neenakost
51.1591
3Greek (el)
Ανισότητα Κωσύ-Σβαρτς
41.3003
4Serbian (sr)
Коши-Шварцова неједнакост
34.2309
5Indonesian (id)
Pertidaksamaan Cauchy–Schwarz
27.8145
6French (fr)
Inégalité de Cauchy-Schwarz
27.4558
7Chinese (zh)
柯西-施瓦茨不等式
27.0771
8Thai (th)
อสมการโคชี-ชวาร์ซ
25.996
9Vietnamese (vi)
Bất đẳng thức Cauchy–Schwarz
25.8158
10German (de)
Cauchy-Schwarzsche Ungleichung
24.0058
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
5 828 243
2French (fr)
Inégalité de Cauchy-Schwarz
1 074 419
3German (de)
Cauchy-Schwarzsche Ungleichung
976 212
4Vietnamese (vi)
Bất đẳng thức Cauchy–Schwarz
760 877
5Chinese (zh)
柯西-施瓦茨不等式
731 815
6Russian (ru)
Неравенство Коши — Буняковского
674 493
7Japanese (ja)
コーシー=シュワルツの不等式
600 291
8Spanish (es)
Desigualdad de Cauchy-Bunyakovsky-Schwarz
435 071
9Italian (it)
Disuguaglianza di Cauchy-Schwarz
379 173
10Korean (ko)
코시-슈바르츠 부등식
367 068
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 "コーシー=シュワルツの不等式" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Cauchy–Schwarz inequality
25 566
2Russian (ru)
Неравенство Коши — Буняковского
3 777
3German (de)
Cauchy-Schwarzsche Ungleichung
3 641
4Chinese (zh)
柯西-施瓦茨不等式
3 465
5French (fr)
Inégalité de Cauchy-Schwarz
3 210
6Japanese (ja)
コーシー=シュワルツの不等式
2 316
7Vietnamese (vi)
Bất đẳng thức Cauchy–Schwarz
1 292
8Spanish (es)
Desigualdad de Cauchy-Bunyakovsky-Schwarz
1 171
9Polish (pl)
Nierówność Cauchy’ego-Schwarza
884
10Hebrew (he)
אי-שוויון קושי-שוורץ
880
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
296
2German (de)
Cauchy-Schwarzsche Ungleichung
106
3French (fr)
Inégalité de Cauchy-Schwarz
105
4Vietnamese (vi)
Bất đẳng thức Cauchy–Schwarz
81
5Russian (ru)
Неравенство Коши — Буняковского
62
6Italian (it)
Disuguaglianza di Cauchy-Schwarz
49
7Chinese (zh)
柯西-施瓦茨不等式
45
8Dutch (nl)
Ongelijkheid van Cauchy-Schwarz
43
9Norwegian (no)
Cauchy–Schwarz’ ulikhet
41
10Hungarian (hu)
Cauchy–Bunyakovszkij–Schwarz-egyenlőtlenség
40
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 "コーシー=シュワルツの不等式" with the highest AI in June 2025
#LanguageAI awardRelative AI
1French (fr)
Inégalité de Cauchy-Schwarz
2
2Ukrainian (uk)
Нерівність Коші — Буняковського
2
3German (de)
Cauchy-Schwarzsche Ungleichung
1
4English (en)
Cauchy–Schwarz inequality
1
5Indonesian (id)
Pertidaksamaan Cauchy–Schwarz
1
6Urdu (ur)
کاشی شوارز نامساوات
1
7Arabic (ar)
متباينة كوشي-شفارتس
0
8Belarusian (be)
Няроўнасць Кашы — Бунякоўскага
0
9Catalan (ca)
Desigualtat de Cauchy-Schwarz
0
10Czech (cs)
Cauchyho–Schwarzova nerovnost
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
300
2Japanese (ja)
コーシー=シュワルツの不等式
201
3Italian (it)
Disuguaglianza di Cauchy-Schwarz
158
4Chinese (zh)
柯西-施瓦茨不等式
129
5French (fr)
Inégalité de Cauchy-Schwarz
103
6Hebrew (he)
אי-שוויון קושי-שוורץ
87
7German (de)
Cauchy-Schwarzsche Ungleichung
80
8Ukrainian (uk)
Нерівність Коші — Буняковського
71
9Korean (ko)
코시-슈바르츠 부등식
42
10Russian (ru)
Неравенство Коши — Буняковского
39
More...

Scores

Estimated value for Wikipedia:
Japanese:
Global:
Popularity in June 2025:
Japanese:
Global:
Popularity in all years:
Japanese:
Global:
Authors in June 2025:
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:
#40039
06.2021
Global:
#16804
10.2021

AI rank trends

Best Rank Japanese:
#1467
05.2019
Global:
#490
08.2001

Local AI rank history

Global AI rank history

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Cauchy–Schwarz inequality from Wikipedia articles about Hölders inequality, Cauchys inequality, Triangle inequality, Inequality and AM–GM 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 Viktor Bunyakovsky.

Cumulative results of quality and popularity of the Wikipedia article

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

News from 12 August 2025

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In Japanese Wikipedia the most popular articles on that day were: 日本航空123便墜落事故, 坂本九, 二階堂ふみ, カズレーザー, 北原遥子, やなせたかし, 柏木由紀子, 大竹七未, 大島花子, 舞坂ゆき子.

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