Skaler çarpma

Skaler çarpım ile karıştırılmamalıdır.
Örnek olarak bir a vektörünün, 2 ve -1 skalerleri ile skaler çarpması sonucu elde edilen 2a ve -a vektörleri.

Matematikte skaler çarpma, vektör uzayında tanımlanan temel işlemlerden biridir. Daha genel bir tanımla, soyut cebirdeki bir modüldür. Sezgisel geometrik bağlamda, bir reel vektörü pozitif reel sayı çarpanları ile skaler çarpma, vektörün yönünü değiştirmeksizin yalnızca büyüklüğünü değiştirir. Skaler terimi bu kullanımdan türetilmiştir: Bir skaler, vektörlerin ölçeklendirme işlemidir. Bir vektörün skaler (burada nokta bir vektördür) ile çarpılması olan skaler çarpma ile, iki vektörün (burada nokta bir skalerdir) iç çarpımı birbirinden ayırt edilmelidir.

Tanım

Eğer K, bir alan ve V, K üzerinde bir vektör uzayı olursa, bu durumda skaler çarpma, K × V den V ye bir fonksiyon olur. Sonuçta bu fonksiyon, K da c, V de v olur ve cv ile ifade edilir.

Özellikler

Skaler çarpma, aşağıdaki işlemlerde geçerlidir. (vektör kalın harfle yazılmıştır):

  • Skalerde toplama: (c + d)v = cv + dv;
  • Vektörde toplama: c(v + w) = cv + cw;
  • Skalerlerin, skaler çarpma işlemi ile nokta uyumluluğu: (cd)v = c(dv);
  • 1 ile çarpma vektörü değiştirmez: 1v = v;
  • 0 ile çarpma sıfır vektörünü verir: 0v = 0;
  • -1 ile çarpma toplamanın tersini verir: (−1)v = −v.

Burada +, ya alanda ya da vektör uzayında toplama işlemidir. Sıfır toplama birimidir. Hem skaler çarpma hem de çarpma işlemi aynı biçimde gösterilir.

Read other articles:

Guinea Portugis

Provinsi Seberang Laut GuineaProvíncia Portuguesa de Guiné1588–1974 Bendera Lambang Lagu kebangsaan: Hymno Patriótico (1808–26)Lagu PatriotikHino da Carta (1826–1911)Himne PiagamA Portuguesa (1911–74)PortugisStatus Jajahan Tanjung Verde Portugis (1588–1879) Koloni Kekaisaran Portugis (1879–1951) Provinsi Seberang Laut Portugis (1951–1973) Negara Bagian Kekaisaran Portugis (1973–1974) Ibu kotaBolama (1852–1942)Bissau (1942–1974)Bahasa yang umum digunakanPortugi...

 

1928 United States Senate special election in Ohio

Not to be confused with 1928 United States Senate election in Ohio. 1928 United States Senate special election in Ohio ← 1926 November 6, 1928 1930 (special) →   Nominee Theodore E. Burton Graham P. Hunt Party Republican Democratic Popular vote 1,429,554 856,807 Percentage 62.43% 37.42% U.S. senator before election Cyrus Locher Democratic Elected U.S. Senator Theodore E. Burton Republican Elections in Ohio Federal government U.S. President 1804 1808 1812 1816 ...

 

فيليبو إنزاغي

فيليبو إنزاغي (بالإيطالية: Filippo Inzaghi)‏ إنزاغي في عام 2011. معلومات شخصية الاسم الكامل فيليبو إنزاغي[1] الميلاد 9 أغسطس 1973 (العمر 50 سنة)[1][2]بياتشنزا، إيطاليا الطول 1.81 م (5 قدم 11 1⁄2 بوصة)[2] مركز اللعب مهاجم الجنسية إيطالي اللقب بيبو، سوبر بيبو أخوة وأخ�...

Tour d'Abou Dabi 2018

Tour d'Abou Dabi 2018 GénéralitésCourse4e Tour d'Abou DabiCompétitionUCI World Tour 2018 2.UWTÉtapes5Dates21 – 25 février 2018Distance687,6 kmPays Émirats arabes unisLieu de départMadinat ZayedLieu d'arrivéeJebel HafeetÉquipes20Partants139Arrivants132Vitesse moyenne42,966 km/hSite officielSite officielRésultatsVainqueur Alejandro Valverde (Movistar Team)Deuxième Wilco Kelderman (Team Sunweb)Troisième Miguel Ángel López (Astana)Classement par points Elia Viviani (Quick-Step Fl...

 

Gruppo d'armate

Unità militari Unità Numero di soldati Grado del comandante Gruppo di fuoco 2-5 Caporale SquadraCarroPezzo 10-151 carro1 pezzo Caporal maggiore,Sergente PlotonePlotone carriSezione 30-504 carri2 o più pezzi Maresciallo,Sottotenente,Tenente CompagniaSquadroneBatteria 100-25010-20 carrivariabile Tenente,Capitano BattaglioneGruppo 500-1.000 Maggiore,Tenente colonnello, Reggimento 1.500-3.000 Colonnello Brigata 4.000-6.000 Generale di brigata Divisione 10.00030.000 Generale di divisione Corpo...

 

コルク

この記事は検証可能な参考文献や出典が全く示されていないか、不十分です。出典を追加して記事の信頼性向上にご協力ください。（このテンプレートの使い方）出典検索?: コルク – ニュース · 書籍 · スカラー · CiNii · J-STAGE · NDL · dlib.jp · ジャパンサーチ · TWL（2017年4月） コルクを打ち抜いて作った瓶の栓 コルク（木栓、�...

Élections régionales togolaises de 2024

Cet article ou cette section contient des informations sur un scrutin récent ou en cours. Il se peut que ces informations soient de nature spéculative et que leur teneur change considérablement alors que le scrutin approche puis passe.La dernière modification de cette page a été faite le 7 mai 2024 à 15:12. Élections régionales togolaises de 2024 179 sièges de conseillers régionaux 29 avril 2024 Union pour la République – Faure Gnassingbé Sièges obtenus 137 Alliance...

 

Emma de Normandie

Pour les articles homonymes, voir Emma. Emma de Normandie Emma de Normandie reçoit le manuscrit de l'Encomium Emmae Reginae des mains de son auteur, vers 1041-1042. Ses fils Édouard le Confesseur et Harthaknut sont à l’arrière-plan.Titres Reine consort d'Angleterre 1002 – 1013 Données clés Prédécesseur Ælfgifu d'York Successeur Świętosława Reine consort d'Angleterre 1014 – 23 avril 1016 Données clés Prédécesseur Świętosława Successeur Ealdgyth Reine consort d'Ang...

 

2016年美國總統選舉

2016年美國總統選舉 ← 2012 2016年11月8日 2020 → 538個選舉人團席位獲勝需270票民意調查投票率55.7%[1][2] ▲ 0.8 %   获提名人 唐納·川普 希拉莉·克林頓 政党 共和黨 民主党 家鄉州 紐約州 紐約州 竞选搭档 迈克·彭斯 蒂姆·凱恩 选举人票 304[3][4][註 1] 227[5] 胜出州/省 30 + 緬-2 20 + DC 民選得票 62,984,828[6] 65,853,514[6]...

Fantasy football (gridiron)

Reality-based football gameAn example of a fantasy football matchup hosted and scored on the ESPN Fantasy app Fantasy football is a game in which the participants serve as owners and general managers of virtual professional American football teams. The competitors select their rosters by participating in a draft in which all relevant National Football League (NFL) players are available. Fantasy points are awarded in weekly matchups based on the actual performances of football players in real-...

 

أوتوبليندا 41

أوتوبليندا 41 AB 41 في شمال أفريقيا. النوع عربة مدرعة بلد الأصل إيطاليا تاريخ الاستخدام فترة الاستخدام 1941-1945 المستخدمون الجيش الملكي الإيطالي فيرماخت الحروب الحرب العالمية الثانية تاريخ الصنع صمم 1940 المصنع أنزالدو - فوساتي [1] صنع 1941-1943 الكمية المصنوعة 550 فئات أخرى AS 42 كام�...

 

معهد الدراسات السياسية بباريس

معهد الدراسات السياسية شعار معهد الدراسات السياسية بباريس   معلومات التأسيس 1872 النوع جامعة حكومية وخاصة التوجهات الدراسية العلوم السياسية، العلاقات الدولية، القانون، العلوم السياسية، التسويق، التمويل، إدارة الموارد البشرية، الاتصال، التخطيط العمراني، الصحافة المو...

NGC 4202

NGC 4202   الكوكبة العذراء[1]  رمز الفهرس NGC 4202 (الفهرس العام الجديد)MCG+00-31-046 (فهرس المجرات الموروفولوجي)PGC 39495 (فهرس المجرات الرئيسية)2MASX J12180856-0103506 (Two Micron All-Sky Survey, Extended source catalogue)UGC 7337 (فهرس أوبسالا العام)GSC 04940-00085 (دليل النجم المفهرس)GAMA 32362 (Galaxy And Mass Assembly survey)2dFGRS TGN248Z126 (مسح ال�...

 

François Guizot

French historian, orator and statesman (1787–1874) François GuizotPortrait by Jehan Georges Vibert, after an 1837 original by Paul DelarochePrime Minister of FranceIn office18 September 1847 – 23 February 1848MonarchLouis Philippe IPreceded byJean-de-Dieu SoultSucceeded byJacques-Charles DupontMinister of Foreign AffairsIn office29 October 1840 – 23 February 1848Prime MinisterJean-de-Dieu SoultPreceded byAdolphe ThiersSucceeded byAlphonse de LamartineMinister of Publi...

 

ديربي الميرسيسايد

ديربي الميرسيسايد أسماء أخرىديربي ليفربولالموقع إنجلترا (ليفربول)الفرق المتنافسةليفربول إيفرتونأول لقاءإيفرتون 3-0 ليفربول الدوري الإنجليري 1894-95 (13 أكتوبر 1894)عدد المواجهات500الأكثر فوزًا[[ نادي ليفربول ]] (97)الأكثر ظهورًا نيفيل ساوثهول (44)الأكثر تسجيلًا إيان راش (25)آخر لق�...

Church of Sweden

Evangelical Lutheran church Church of SwedenSvenska kyrkanArms of the Church of Sweden with its centred crown, representing both the victory of Christ over death[1] and the crown of Erik the Holy,[2] Patron Saint of Sweden.TypeCommunionClassificationProtestantOrientationLutheranScriptureBibleTheologyFolk ChurchHigh Church LutheranismEvangelical Catholic[3]PolityEpiscopalGovernanceGeneral SynodPrimateMartin ModéusAssociationsLutheran World FederationWorld Council of Ch...

 

Popular Conservatism

Right-wing British political group Popular ConservatismFormationFebruary 6, 2024; 3 months ago (2024-02-06)PurposeConservatismRight libertarianismDirectorMark LittlewoodWebsitewww.popularconservatism.com Popular Conservatism or PopCon, is a right-wing faction within the British Conservative Party.[1] The director of the group is Mark Littlewood, who is an ally of the former prime minister Liz Truss.[2] Ideology The group is ideologically on the right-wing of ...

 

Effective temperature

Temperature of a black body that would emit the same total amount of electromagnetic radiation The effective temperature of a body such as a star or planet is the temperature of a black body that would emit the same total amount of electromagnetic radiation.[1][2] Effective temperature is often used as an estimate of a body's surface temperature when the body's emissivity curve (as a function of wavelength) is not known. When the star's or planet's net emissivity in the releva...

Archaeology (album)

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Archaeology album – news · newspapers · books · scholar · JSTOR (September 2012) (Learn how and when to remove this message) 1996 studio album by The RutlesArchaeologyStudio album by The RutlesReleased29 October 1996Recorded1978, 1996GenreComedyLe...

 

Grotesque

Art style For other uses, see Grotesque (disambiguation). Grotesque studies, Michelangelo Since at least the 18th century (in French and German, as well as English), grotesque has come to be used as a general adjective for the strange, mysterious, magnificent, fantastic, hideous, ugly, incongruous, unpleasant, or disgusting, and thus is often used to describe weird shapes and distorted forms such as Halloween masks. In art, performance, and literature, however, grotesque may also refer to som...