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mw-first-heading"><span class="mw-page-title-main">Multiplicação escalar</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Ir para um artigo noutra língua. 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href="https://de.wikipedia.org/wiki/Skalarmultiplikation" title="Skalarmultiplikation — alemão" lang="de" hreflang="de" data-title="Skalarmultiplikation" data-language-autonym="Deutsch" data-language-local-name="alemão" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%92%CE%B1%CE%B8%CE%BC%CF%89%CF%84%CF%8C%CF%82_%CF%80%CE%BF%CE%BB%CE%BB%CE%B1%CF%80%CE%BB%CE%B1%CF%83%CE%B9%CE%B1%CF%83%CE%BC%CF%8C%CF%82" title="Βαθμωτός πολλαπλασιασμός — grego" lang="el" hreflang="el" data-title="Βαθμωτός πολλαπλασιασμός" data-language-autonym="Ελληνικά" data-language-local-name="grego" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Scalar_multiplication" title="Scalar multiplication — inglês" lang="en" hreflang="en" data-title="Scalar multiplication" data-language-autonym="English" data-language-local-name="inglês" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Skalara_multipliko" title="Skalara multipliko — esperanto" lang="eo" hreflang="eo" data-title="Skalara multipliko" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Multiplicaci%C3%B3n_escalar" title="Multiplicación escalar — espanhol" lang="es" hreflang="es" data-title="Multiplicación escalar" data-language-autonym="Español" data-language-local-name="espanhol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B6%D8%B1%D8%A8_%D9%86%D8%B1%D8%AF%D9%87%E2%80%8C%D8%A7%DB%8C" title="ضرب نرده‌ای — persa" lang="fa" hreflang="fa" data-title="ضرب نرده‌ای" data-language-autonym="فارسی" data-language-local-name="persa" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Multiplication_par_un_scalaire" title="Multiplication par un scalaire — francês" lang="fr" hreflang="fr" data-title="Multiplication par un scalaire" data-language-autonym="Français" data-language-local-name="francês" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9B%D7%A4%D7%9C_%D7%91%D7%A1%D7%A7%D7%9C%D7%A8" title="כפל בסקלר — hebraico" lang="he" hreflang="he" data-title="כפל בסקלר" data-language-autonym="עברית" data-language-local-name="hebraico" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Perkalian_skalar" title="Perkalian skalar — indonésio" lang="id" hreflang="id" data-title="Perkalian skalar" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonésio" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%8A%A4%EC%B9%BC%EB%9D%BC_%EA%B3%B1%EC%85%88" title="스칼라 곱셈 — coreano" lang="ko" hreflang="ko" data-title="스칼라 곱셈" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pendaraban_skalar" title="Pendaraban skalar — malaio" lang="ms" hreflang="ms" data-title="Pendaraban skalar" data-language-autonym="Bahasa Melayu" data-language-local-name="malaio" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Scalaire_vermenigvuldiging" title="Scalaire vermenigvuldiging — neerlandês" lang="nl" hreflang="nl" data-title="Scalaire vermenigvuldiging" data-language-autonym="Nederlands" data-language-local-name="neerlandês" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Mno%C5%BCenie_przez_skalar" title="Mnożenie przez skalar — polaco" lang="pl" hreflang="pl" data-title="Mnożenie przez skalar" data-language-autonym="Polski" data-language-local-name="polaco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/%C3%8Enmul%C8%9Birea_cu_un_scalar" title="Înmulțirea cu un scalar — romeno" lang="ro" hreflang="ro" data-title="Înmulțirea cu un scalar" data-language-autonym="Română" data-language-local-name="romeno" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru badge-Q70894304 mw-list-item" title=""><a href="https://ru.wikipedia.org/wiki/%D0%A3%D0%BC%D0%BD%D0%BE%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5_%D0%BD%D0%B0_%D1%81%D0%BA%D0%B0%D0%BB%D1%8F%D1%80" title="Умножение на скаляр — russo" lang="ru" hreflang="ru" data-title="Умножение на скаляр" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Mno%C5%BEenje_vektorja_s_%C5%A1tevilom" title="Množenje vektorja s številom — esloveno" lang="sl" hreflang="sl" data-title="Množenje vektorja s številom" data-language-autonym="Slovenščina" data-language-local-name="esloveno" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Shum%C3%ABzimi_skalar" title="Shumëzimi skalar — albanês" lang="sq" hreflang="sq" data-title="Shumëzimi skalar" data-language-autonym="Shqip" data-language-local-name="albanês" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%A4%E0%AE%BF%E0%AE%9A%E0%AF%88%E0%AE%AF%E0%AE%BF%E0%AE%B2%E0%AE%BF_%E0%AE%AA%E0%AF%86%E0%AE%B0%E0%AF%81%E0%AE%95%E0%AF%8D%E0%AE%95%E0%AE%B2%E0%AF%8D" title="திசையிலி பெருக்கல் — tâmil" lang="ta" hreflang="ta" data-title="திசையிலி பெருக்கல்" data-language-autonym="தமிழ்" data-language-local-name="tâmil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Skaler_%C3%A7arpma" title="Skaler çarpma — turco" lang="tr" hreflang="tr" data-title="Skaler çarpma" data-language-autonym="Türkçe" 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class="reference"><a href="#cite_note-2"><span>[</span>2<span>]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span>[</span>3<span>]</span></a></sup> ou mais geralmente, um <a href="/wiki/M%C3%B3dulo_(%C3%A1lgebra)" title="Módulo (álgebra)">módulo</a> em <a href="/wiki/%C3%81lgebra_abstrata" title="Álgebra abstrata">álgebra abstrata</a>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span>[</span>4<span>]</span></a></sup><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span>[</span>5<span>]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Definição"><span id="Defini.C3.A7.C3.A3o"></span>Definição</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Multiplica%C3%A7%C3%A3o_escalar&veaction=edit&section=1" title="Editar secção: Definição" class="mw-editsection-visualeditor"><span>editar</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Multiplica%C3%A7%C3%A3o_escalar&action=edit&section=1" title="Editar código-fonte da secção: Definição"><span>editar código-fonte</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Em geral, se <i>K</i> é um <a href="/wiki/Corpo_(matem%C3%A1tica)" title="Corpo (matemática)">campo</a> e <i>V</i> é um espaço vetorial sobre <i>K</i>, então a multiplicação escalar é uma <a href="/wiki/Fun%C3%A7%C3%A3o_(matem%C3%A1tica)" title="Função (matemática)">função</a> de <i>K</i> x <i>V</i> para <i>V</i>. O resultado da aplicação dessa função para <i>c</i> em <i>K</i> e <i>v</i> em <i>V</i> é denotado <i>cv</i>. </p> <h2 id="Referências" style="cursor: help;" title="Esta seção foi configurada para não ser editável diretamente. Edite a página toda ou a seção anterior em vez disso."><span id="Refer.C3.AAncias"></span>Referências</h2> <div class="reflist" style="list-style-type: decimal;"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text"><cite class="citation book">Lay, David C. (2006). <i>Linear Algebra and Its Applications</i> 3rd ed. [S.l.]: Addison–Wesley. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Especial:Fontes_de_livros/0-321-28713-4" title="Especial:Fontes de livros/0-321-28713-4">0-321-28713-4</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3AMultiplica%C3%A7%C3%A3o+escalar&rft.aufirst=David+C.&rft.aulast=Lay&rft.btitle=Linear+Algebra+and+Its+Applications&rft.date=2006&rft.edition=3rd&rft.genre=book&rft.isbn=0-321-28713-4&rft.pub=Addison%93Wesley&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><cite class="citation book"><a href="/wiki/Gilbert_Strang" title="Gilbert Strang">Strang, Gilbert</a> (2006). <i>Linear Algebra and Its Applications</i> 4th ed. [S.l.]: Brooks Cole. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Especial:Fontes_de_livros/0-03-010567-6" title="Especial:Fontes de livros/0-03-010567-6">0-03-010567-6</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3AMultiplica%C3%A7%C3%A3o+escalar&rft.aufirst=Gilbert&rft.aulast=Strang&rft.btitle=Linear+Algebra+and+Its+Applications&rft.date=2006&rft.edition=4th&rft.genre=book&rft.isbn=0-03-010567-6&rft.pub=Brooks+Cole&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><cite class="citation book">Axler, Sheldon (2002). <i>Linear Algebra Done Right</i> 2nd ed. [S.l.]: <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer</a>. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Especial:Fontes_de_livros/0-387-98258-2" title="Especial:Fontes de livros/0-387-98258-2">0-387-98258-2</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3AMultiplica%C3%A7%C3%A3o+escalar&rft.aufirst=Sheldon&rft.aulast=Axler&rft.btitle=Linear+Algebra+Done+Right&rft.date=2002&rft.edition=2nd&rft.genre=book&rft.isbn=0-387-98258-2&rft.pub=Springer&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text"><cite class="citation book">Dummit, David S.; Foote, Richard M. (2004). <i>Abstract Algebra</i> 3rd ed. [S.l.]: <a href="/wiki/John_Wiley_%26_Sons" title="John Wiley & Sons">John Wiley & Sons</a>. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Especial:Fontes_de_livros/0-471-43334-9" title="Especial:Fontes de livros/0-471-43334-9">0-471-43334-9</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3AMultiplica%C3%A7%C3%A3o+escalar&rft.au=Foote%2C+Richard+M.&rft.aufirst=David+S.&rft.aulast=Dummit&rft.btitle=Abstract+Algebra&rft.date=2004&rft.edition=3rd&rft.genre=book&rft.isbn=0-471-43334-9&rft.pub=John+Wiley+%26+Sons&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><cite class="citation book"><a href="/wiki/Serge_Lang" title="Serge Lang">Lang, Serge</a> (2002). <i>Algebra</i>. Col: <a href="/wiki/Graduate_Texts_in_Mathematics" title="Graduate Texts in Mathematics">Graduate Texts in Mathematics</a>. [S.l.]: <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer</a>. <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Especial:Fontes_de_livros/0-387-95385-X" title="Especial:Fontes de livros/0-387-95385-X">0-387-95385-X</a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fpt.wikipedia.org%3AMultiplica%C3%A7%C3%A3o+escalar&rft.aufirst=Serge&rft.aulast=Lang&rft.btitle=Algebra&rft.date=2002&rft.genre=book&rft.isbn=0-387-95385-X&rft.pub=Springer&rft.series=Graduate+Texts+in+Mathematics&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div></div> <table class="noprint" style="border-top:none; border-bottom:none; background:transparent; color: inherit"><tbody><tr> <td style="text-align: center;"><span typeof="mw:File"><a href="/wiki/Ficheiro:E-to-the-i-pi.svg" class="mw-file-description"><img alt="Ícone de esboço" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/34px-E-to-the-i-pi.svg.png" decoding="async" width="34" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/51px-E-to-the-i-pi.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/68px-E-to-the-i-pi.svg.png 2x" data-file-width="512" data-file-height="453" /></a></span></td> <td><i>Este artigo sobre <a href="/wiki/Matem%C3%A1tica" title="Matemática">matemática</a> é um <a href="/wiki/Wikip%C3%A9dia:Esbo%C3%A7o" title="Wikipédia:Esboço">esboço</a>. 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