CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="zh" dir="ltr"> <head> <meta charset="UTF-8"> <title>反射 (数学) - 维基百科，自由的百科全书</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )zhwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"zh", "wgMonthNames":["","1月","2月","3月","4月","5月","6月","7月","8月","9月","10月","11月","12月"],"wgRequestId":"b0497384-fa3a-4310-a384-1e3ac455a4ae","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"反射_(数学)","wgTitle":"反射 (数学)","wgCurRevisionId":71724386,"wgRevisionId":71724386,"wgArticleId":565403,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["函数","欧几里得对称","线性算子"],"wgPageViewLanguage":"zh","wgPageContentLanguage":"zh","wgPageContentModel":"wikitext","wgRelevantPageName":"反射_(数学)","wgRelevantArticleId":565403,"wgUserVariant":"zh","wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0,"wgVisualEditor":{ "pageLanguageCode":"zh","pageLanguageDir":"ltr","pageVariantFallbacks":["zh-hans","zh-hant","zh-cn","zh-tw","zh-hk","zh-sg","zh-mo","zh-my"]},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":3000,"wgRelatedArticlesCompat":[],"wgCentralAuthMobileDomain":false,"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q426221","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.gadget.large-font":"ready","ext.globalCssJs.user.styles":"ready","site.styles":"ready", "user.styles":"ready","ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["mediawiki.page.media","site","mediawiki.page.ready","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.edit0","ext.gadget.WikiMiniAtlas","ext.gadget.UnihanTooltips","ext.gadget.Difflink","ext.gadget.pseudonamespace-UI","ext.gadget.SpecialWikitext","ext.gadget.switcher","ext.gadget.VariantAlly","ext.gadget.AdvancedSiteNotices","ext.gadget.hideConversionTab","ext.gadget.internalLinkHelper-altcolor","ext.gadget.noteTA","ext.gadget.NavFrame","ext.gadget.collapsibleTables","ext.gadget.scrollUpButton","ext.urlShortener.toolbar", "ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=zh&modules=ext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=zh&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=zh&modules=ext.gadget.large-font&only=styles&skin=vector-2022"> <link rel="stylesheet" href="/w/load.php?lang=zh&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.4"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/a/ae/Simx2%3DtraslOK.png"> <meta property="og:image:width" content="1200"> <meta property="og:image:height" content="1200"> <meta property="og:image" content="https://upload.wikimedia.org/wikipedia/commons/a/ae/Simx2%3DtraslOK.png"> <meta property="og:image:width" content="800"> <meta property="og:image:height" content="800"> <meta property="og:image:width" content="640"> <meta property="og:image:height" content="640"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="反射 (数学) - 维基百科，自由的百科全书"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//zh.m.wikipedia.org/wiki/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)"> <link rel="alternate" type="application/x-wiki" title="编辑本页" href="/w/index.php?title=%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (zh)"> <link rel="EditURI" type="application/rsd+xml" href="//zh.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://zh.wikipedia.org/wiki/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)"> <link rel="alternate" hreflang="zh" href="https://zh.wikipedia.org/wiki/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)"> <link rel="alternate" hreflang="zh-Hans" href="https://zh.wikipedia.org/zh-hans/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)"> <link rel="alternate" hreflang="zh-Hans-CN" href="https://zh.wikipedia.org/zh-cn/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)"> <link rel="alternate" hreflang="zh-Hans-MY" href="https://zh.wikipedia.org/zh-my/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)"> <link rel="alternate" hreflang="zh-Hans-SG" href="https://zh.wikipedia.org/zh-sg/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)"> <link rel="alternate" hreflang="zh-Hant" href="https://zh.wikipedia.org/zh-hant/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)"> <link rel="alternate" hreflang="zh-Hant-HK" href="https://zh.wikipedia.org/zh-hk/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)"> <link rel="alternate" hreflang="zh-Hant-MO" href="https://zh.wikipedia.org/zh-mo/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)"> <link rel="alternate" hreflang="zh-Hant-TW" href="https://zh.wikipedia.org/zh-tw/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)"> <link rel="alternate" hreflang="x-default" href="https://zh.wikipedia.org/wiki/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.zh"> <link rel="alternate" type="application/atom+xml" title="Wikipedia的Atom feed" href="/w/index.php?title=Special:%E6%9C%80%E8%BF%91%E6%9B%B4%E6%94%B9&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-反射_数学 rootpage-反射_数学 skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">跳转到内容</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="站点"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="主菜单" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">主菜单</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">主菜单</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">隐藏</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> 导航 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Wikipedia:%E9%A6%96%E9%A1%B5" title="访问首页[z]" accesskey="z"><span>首页</span></a></li><li id="n-indexpage" class="mw-list-item"><a href="/wiki/Wikipedia:%E5%88%86%E7%B1%BB%E7%B4%A2%E5%BC%95" title="以分类索引搜寻中文维基百科"><span>分类索引</span></a></li><li id="n-Featured_content" class="mw-list-item"><a href="/wiki/Portal:%E7%89%B9%E8%89%B2%E5%85%A7%E5%AE%B9" title="查看中文维基百科的特色内容"><span>特色内容</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:%E6%96%B0%E8%81%9E%E5%8B%95%E6%85%8B" title="提供当前新闻事件的背景资料"><span>新闻动态</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:%E6%9C%80%E8%BF%91%E6%9B%B4%E6%94%B9" title="列出维基百科中的最近修改[r]" accesskey="r"><span>最近更改</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:%E9%9A%8F%E6%9C%BA%E9%A1%B5%E9%9D%A2" title="随机载入一个页面[x]" accesskey="x"><span>随机条目</span></a></li> </ul> </div> </div> <div id="p-help" class="vector-menu mw-portlet mw-portlet-help" > <div class="vector-menu-heading"> 帮助 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:%E7%9B%AE%E5%BD%95" title="寻求帮助"><span>帮助</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:%E7%A4%BE%E7%BE%A4%E9%A6%96%E9%A1%B5" title="关于本计划、你可以做什么、应该如何做"><span>维基社群</span></a></li><li id="n-policy" class="mw-list-item"><a href="/wiki/Wikipedia:%E6%96%B9%E9%87%9D%E8%88%87%E6%8C%87%E5%BC%95" title="查看维基百科的方针和指引"><span>方针与指引</span></a></li><li id="n-villagepump" class="mw-list-item"><a href="/wiki/Wikipedia:%E4%BA%92%E5%8A%A9%E5%AE%A2%E6%A0%88" title="参与维基百科社群的讨论"><span>互助客栈</span></a></li><li id="n-Information_desk" class="mw-list-item"><a href="/wiki/Wikipedia:%E7%9F%A5%E8%AF%86%E9%97%AE%E7%AD%94" title="解答任何与维基百科无关的问题的地方"><span>知识问答</span></a></li><li id="n-conversion" class="mw-list-item"><a href="/wiki/Wikipedia:%E5%AD%97%E8%AF%8D%E8%BD%AC%E6%8D%A2" title="提出字词转换请求"><span>字词转换</span></a></li><li id="n-IRC" class="mw-list-item"><a href="/wiki/Wikipedia:IRC%E8%81%8A%E5%A4%A9%E9%A2%91%E9%81%93"><span>IRC即时聊天</span></a></li><li id="n-contact" class="mw-list-item"><a href="/wiki/Wikipedia:%E8%81%94%E7%BB%9C%E6%88%91%E4%BB%AC" title="如何联络维基百科"><span>联络我们</span></a></li><li id="n-about" class="mw-list-item"><a href="/wiki/Wikipedia:%E5%85%B3%E4%BA%8E" title="查看维基百科的简介"><span>关于维基百科</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Wikipedia:%E9%A6%96%E9%A1%B5" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="维基百科" src="/static/images/mobile/copyright/wikipedia-wordmark-zh.svg" style="width: 6.5625em; height: 1.375em;"> <img class="mw-logo-tagline" alt="自由的百科全书" src="/static/images/mobile/copyright/wikipedia-tagline-zh.svg" width="103" height="14" style="width: 6.4375em; height: 0.875em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:%E6%90%9C%E7%B4%A2" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="搜索维基百科[f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>搜索</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="搜索维基百科" aria-label="搜索维基百科" autocapitalize="sentences" title="搜索维基百科[f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:搜索"> </div> <button class="cdx-button cdx-search-input__end-button">搜索</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="个人工具"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="外观"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="更改页面字体大小、宽度和颜色的外观" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="外观" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">外观</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?utm_source=donate&utm_medium=sidebar&utm_campaign=spontaneous&uselang=zh-hans" class=""><span>资助维基百科</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:%E5%88%9B%E5%BB%BA%E8%B4%A6%E6%88%B7&returnto=%E5%8F%8D%E5%B0%84+%28%E6%95%B0%E5%AD%A6%29" title="我们推荐您创建账号并登录，但这不是强制性的" class=""><span>创建账号</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:%E7%94%A8%E6%88%B7%E7%99%BB%E5%BD%95&returnto=%E5%8F%8D%E5%B0%84+%28%E6%95%B0%E5%AD%A6%29" title="建议你登录，尽管并非必须。[o]" accesskey="o" class=""><span>登录</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="更多选项" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="个人工具" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">个人工具</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="用户菜单" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?utm_source=donate&utm_medium=sidebar&utm_campaign=spontaneous&uselang=zh-hans"><span>资助维基百科</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E5%88%9B%E5%BB%BA%E8%B4%A6%E6%88%B7&returnto=%E5%8F%8D%E5%B0%84+%28%E6%95%B0%E5%AD%A6%29" title="我们推荐您创建账号并登录，但这不是强制性的"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>创建账号</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E7%94%A8%E6%88%B7%E7%99%BB%E5%BD%95&returnto=%E5%8F%8D%E5%B0%84+%28%E6%95%B0%E5%AD%A6%29" title="建议你登录，尽管并非必须。[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>登录</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 未登录编辑者的页面 <a href="/wiki/Help:%E6%96%B0%E6%89%8B%E5%85%A5%E9%97%A8" aria-label="了解有关编辑的更多信息"><span>了解详情</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%B4%A1%E7%8C%AE" title="来自此IP地址的编辑列表[y]" accesskey="y"><span>贡献</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%AE%A8%E8%AE%BA%E9%A1%B5" title="对于来自此IP地址编辑的讨论[n]" accesskey="n"><span>讨论</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="站点"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目录" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">序言</div> </a> </li> <li id="toc-豪斯霍尔德变换" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#豪斯霍尔德变换"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>豪斯霍尔德变换</span> </div> </a> <ul id="toc-豪斯霍尔德变换-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-参见" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#参见"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>参见</span> </div> </a> <ul id="toc-参见-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-外部链接" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#外部链接"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>外部链接</span> </div> </a> <ul id="toc-外部链接-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="目录" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="开关目录" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">开关目录</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">反射 (数学)</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="前往另一种语言写成的文章。26种语言可用" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-26" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">26种语言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%86%D8%B9%D9%83%D8%A7%D8%B3_(%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA)" title="انعكاس (رياضيات) – 阿拉伯语" lang="ar" hreflang="ar" data-title="انعكاس (رياضيات)" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9E%D1%82%D1%80%D0%B0%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Отражение (математика) – 保加利亚语" lang="bg" hreflang="bg" data-title="Отражение (математика)" data-language-autonym="Български" data-language-local-name="保加利亚语" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Reflexi%C3%B3_(matem%C3%A0tiques)" title="Reflexió (matemàtiques) – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Reflexió (matemàtiques)" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A1%D1%83%D0%BB%C4%83%D0%BD%D1%83_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8)" title="Сулăну (геометри) – 楚瓦什语" lang="cv" hreflang="cv" data-title="Сулăну (геометри)" data-language-autonym="Чӑвашла" data-language-local-name="楚瓦什语" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Spiegelung_(Geometrie)" title="Spiegelung (Geometrie) – 德语" lang="de" hreflang="de" data-title="Spiegelung (Geometrie)" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Reflection_(mathematics)" title="Reflection (mathematics) – 英语" lang="en" hreflang="en" data-title="Reflection (mathematics)" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Reflexi%C3%B3n_(matem%C3%A1tica)" title="Reflexión (matemática) – 西班牙语" lang="es" hreflang="es" data-title="Reflexión (matemática)" data-language-autonym="Español" data-language-local-name="西班牙语" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Peegeldus" title="Peegeldus – 爱沙尼亚语" lang="et" hreflang="et" data-title="Peegeldus" data-language-autonym="Eesti" data-language-local-name="爱沙尼亚语" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Peilaus" title="Peilaus – 芬兰语" lang="fi" hreflang="fi" data-title="Peilaus" data-language-autonym="Suomi" data-language-local-name="芬兰语" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A9%D7%99%D7%A7%D7%95%D7%A3_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="שיקוף (מתמטיקה) – 希伯来语" lang="he" hreflang="he" data-title="שיקוף (מתמטיקה)" data-language-autonym="עברית" data-language-local-name="希伯来语" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/T%C3%BCkr%C3%B6z%C3%A9s_(matematika)" title="Tükrözés (matematika) – 匈牙利语" lang="hu" hreflang="hu" data-title="Tükrözés (matematika)" data-language-autonym="Magyar" data-language-local-name="匈牙利语" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Riflessione_(geometria)" title="Riflessione (geometria) – 意大利语" lang="it" hreflang="it" data-title="Riflessione (geometria)" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%8F%A1%E6%98%A0" title="鏡映 – 日语" lang="ja" hreflang="ja" data-title="鏡映" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B0%98%EC%82%AC_(%EA%B8%B0%ED%95%98%ED%95%99)" title="반사 (기하학) – 韩语" lang="ko" hreflang="ko" data-title="반사 (기하학)" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Spiegeling_(meetkunde)" title="Spiegeling (meetkunde) – 荷兰语" lang="nl" hreflang="nl" data-title="Spiegeling (meetkunde)" data-language-autonym="Nederlands" data-language-local-name="荷兰语" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Refleksjon_i_matematikk" title="Refleksjon i matematikk – 挪威尼诺斯克语" lang="nn" hreflang="nn" data-title="Refleksjon i matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="挪威尼诺斯克语" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Reflex%C3%A3o_(matem%C3%A1tica)" title="Reflexão (matemática) – 葡萄牙语" lang="pt" hreflang="pt" data-title="Reflexão (matemática)" data-language-autonym="Português" data-language-local-name="葡萄牙语" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Reflexie_(matematic%C4%83)" title="Reflexie (matematică) – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Reflexie (matematică)" data-language-autonym="Română" data-language-local-name="罗马尼亚语" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9E%D1%82%D1%80%D0%B0%D0%B6%D0%B5%D0%BD%D0%B8%D0%B5_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F)" title="Отражение (геометрия) – 俄语" lang="ru" hreflang="ru" data-title="Отражение (геометрия)" data-language-autonym="Русский" data-language-local-name="俄语" 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/Zrcaljenje" title="Zrcaljenje – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Zrcaljenje" data-language-autonym="Slovenščina" data-language-local-name="斯洛文尼亚语" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%8E%E0%AE%A4%E0%AE%BF%E0%AE%B0%E0%AF%8A%E0%AE%B3%E0%AE%BF%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AF%81_(%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D)" title="எதிரொளிப்பு (கணிதம்) – 泰米尔语" lang="ta" hreflang="ta" data-title="எதிரொளிப்பு (கணிதம்)" data-language-autonym="தமிழ்" data-language-local-name="泰米尔语" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%AA%E0%B8%B0%E0%B8%97%E0%B9%89%E0%B8%AD%E0%B8%99_(%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C)" title="การสะท้อน (คณิตศาสตร์) – 泰语" lang="th" hreflang="th" data-title="การสะท้อน (คณิตศาสตร์)" data-language-autonym="ไทย" data-language-local-name="泰语" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Repleksyon_(matematika)" title="Repleksyon (matematika) – 他加禄语" lang="tl" hreflang="tl" data-title="Repleksyon (matematika)" data-language-autonym="Tagalog" data-language-local-name="他加禄语" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%92%D1%96%D0%B4%D0%B1%D0%B8%D1%82%D1%82%D1%8F_(%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D1%96%D1%8F)" title="Відбиття (геометрія) – 乌克兰语" lang="uk" hreflang="uk" data-title="Відбиття (геометрія)" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/Ph%C3%A9p_ph%E1%BA%A3n_x%E1%BA%A1" title="Phép phản xạ – 越南语" lang="vi" hreflang="vi" data-title="Phép phản xạ" data-language-autonym="Tiếng Việt" data-language-local-name="越南语" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E5%8F%8D%E5%B0%84_(%E6%95%B8%E5%AD%B8)" title="反射 (數學) – 粤语" lang="yue" hreflang="yue" data-title="反射 (數學)" data-language-autonym="粵語" data-language-local-name="粤语" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q426221#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="命名空间"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)" title="浏览条目正文[c]" accesskey="c"><span>条目</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)" rel="discussion" title="关于此页面的讨论[t]" accesskey="t"><span>讨论</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown " > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="更改语言变体" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">不转换</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-varlang-0" class="selected ca-variants-zh mw-list-item"><a href="/zh/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)" lang="zh" hreflang="zh"><span>不转换</span></a></li><li id="ca-varlang-1" class="ca-variants-zh-Hans mw-list-item"><a href="/zh-hans/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)" lang="zh-Hans" hreflang="zh-Hans"><span>简体</span></a></li><li id="ca-varlang-2" class="ca-variants-zh-Hant mw-list-item"><a href="/zh-hant/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)" lang="zh-Hant" hreflang="zh-Hant"><span>繁體</span></a></li><li id="ca-varlang-3" class="ca-variants-zh-Hans-CN mw-list-item"><a href="/zh-cn/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)" lang="zh-Hans-CN" hreflang="zh-Hans-CN"><span>大陆简体</span></a></li><li id="ca-varlang-4" class="ca-variants-zh-Hant-HK mw-list-item"><a href="/zh-hk/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)" lang="zh-Hant-HK" hreflang="zh-Hant-HK"><span>香港繁體</span></a></li><li id="ca-varlang-5" class="ca-variants-zh-Hant-MO mw-list-item"><a href="/zh-mo/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)" lang="zh-Hant-MO" hreflang="zh-Hant-MO"><span>澳門繁體</span></a></li><li id="ca-varlang-6" class="ca-variants-zh-Hans-MY mw-list-item"><a href="/zh-my/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)" lang="zh-Hans-MY" hreflang="zh-Hans-MY"><span>大马简体</span></a></li><li id="ca-varlang-7" class="ca-variants-zh-Hans-SG mw-list-item"><a href="/zh-sg/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)" lang="zh-Hans-SG" hreflang="zh-Hans-SG"><span>新加坡简体</span></a></li><li id="ca-varlang-8" class="ca-variants-zh-Hant-TW mw-list-item"><a href="/zh-tw/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)" lang="zh-Hant-TW" hreflang="zh-Hant-TW"><span>臺灣正體</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="查看"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)"><span>阅读</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)&action=edit" title="编辑该页面[e]" accesskey="e"><span>编辑</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)&action=history" title="本页面的早前版本。[h]" accesskey="h"><span>查看历史</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="页面工具"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="工具" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">工具</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">工具</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">隐藏</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="更多选项" > <div class="vector-menu-heading"> 操作 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)"><span>阅读</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)&action=edit" title="编辑该页面[e]" accesskey="e"><span>编辑</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)&action=history"><span>查看历史</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> 常规 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:%E9%93%BE%E5%85%A5%E9%A1%B5%E9%9D%A2/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)" title="列出所有与本页相链的页面[j]" accesskey="j"><span>链入页面</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:%E9%93%BE%E5%87%BA%E6%9B%B4%E6%94%B9/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)" rel="nofollow" title="页面链出所有页面的更改[k]" accesskey="k"><span>相关更改</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Project:%E4%B8%8A%E4%BC%A0" title="上传图像或多媒体文件[u]" accesskey="u"><span>上传文件</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:%E7%89%B9%E6%AE%8A%E9%A1%B5%E9%9D%A2" title="全部特殊页面的列表[q]" accesskey="q"><span>特殊页面</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)&oldid=71724386" title="此页面该修订版本的固定链接"><span>固定链接</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)&action=info" title="关于此页面的更多信息"><span>页面信息</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:%E5%BC%95%E7%94%A8%E6%AD%A4%E9%A1%B5%E9%9D%A2&page=%E5%8F%8D%E5%B0%84_%28%E6%95%B0%E5%AD%A6%29&id=71724386&wpFormIdentifier=titleform" title="有关如何引用此页面的信息"><span>引用此页</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:URL%E7%BC%A9%E7%9F%AD%E7%A8%8B%E5%BA%8F&url=https%3A%2F%2Fzh.wikipedia.org%2Fwiki%2F%25E5%258F%258D%25E5%25B0%2584_%28%25E6%2595%25B0%25E5%25AD%25A6%29"><span>获取短链接</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fzh.wikipedia.org%2Fwiki%2F%25E5%258F%258D%25E5%25B0%2584_%28%25E6%2595%25B0%25E5%25AD%25A6%29"><span>下载二维码</span></a></li> </ul> </div> </div> <div id="p-electronpdfservice-sidebar-portlet-heading" class="vector-menu mw-portlet mw-portlet-electronpdfservice-sidebar-portlet-heading" > <div class="vector-menu-heading"> 打印/导出 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="electron-print_pdf" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=%E5%8F%8D%E5%B0%84_%28%E6%95%B0%E5%AD%A6%29&action=show-download-screen"><span>下载为PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="javascript:print();" rel="alternate" title="本页面的可打印版本[p]" accesskey="p"><span>打印页面</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> 在其他项目中 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Reflection_(geometry)" hreflang="en"><span>维基共享资源</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q426221" title="链接到连接的数据仓库项目[g]" accesskey="g"><span>维基数据项目</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="页面工具"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="外观"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">外观</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">隐藏</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> <div id="mw-indicator-noteTA-1e95ae6d" class="mw-indicator"><div class="mw-parser-output"><span class="skin-invert" typeof="mw:File"><span title="本页使用了标题或全文手工转换"><img alt="本页使用了标题或全文手工转换" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/35px-Zh_conversion_icon_m.svg.png" decoding="async" width="35" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/53px-Zh_conversion_icon_m.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/70px-Zh_conversion_icon_m.svg.png 2x" data-file-width="32" data-file-height="20" /></span></span></div></div> </div> <div id="siteSub" class="noprint">维基百科，自由的百科全书</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="zh" dir="ltr"><div id="noteTA-1e95ae6d" class="noteTA"><div class="noteTA-title" data-noteta-code="zh-hans:反射 (数学); zh-hant:鏡射 (數學);"></div><div class="noteTA-local"><div data-noteta-code="zh-hans:反射; zh-hant:鏡射;"></div></div></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Simx2%3DtraslOK.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Simx2%3DtraslOK.png/220px-Simx2%3DtraslOK.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/a/ae/Simx2%3DtraslOK.png 1.5x" data-file-width="301" data-file-height="301" /></a><figcaption>在针对一个轴的反射之后的针对另一个平行于前一个轴的轴的反射导致是<a href="/wiki/%E5%B9%B3%E7%A7%BB" title="平移">平移</a>的总和运动</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Simx2%3DrotOK.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Simx2%3DrotOK.png/220px-Simx2%3DrotOK.png" decoding="async" width="220" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Simx2%3DrotOK.png/330px-Simx2%3DrotOK.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Simx2%3DrotOK.png/440px-Simx2%3DrotOK.png 2x" data-file-width="500" data-file-height="500" /></a><figcaption>在针对一个轴的反射之后的针对不平行于前一个轴的反射导致是绕两个轴的交点的<a href="/wiki/%E6%97%8B%E8%BD%AC" title="旋转">旋转</a>的一个总和运动</figcaption></figure> <p>在<a href="/wiki/%E6%95%B0%E5%AD%A6" title="数学">数学</a>中，<b>反射</b>是把一个物体变换成它的<a href="/wiki/%E9%95%9C%E5%83%8F_(%E5%87%A0%E4%BD%95)" title="镜像 (几何)">镜像</a>的<a href="/wiki/%E5%87%BD%E6%95%B0" title="函数">映射</a>。要反射一个平面图形，需要“镜子”是一条直线（反射轴），对于三维空间中的反射就要使用<a href="/wiki/%E5%B9%B3%E9%9D%A2_(%E6%95%B0%E5%AD%A6)" title="平面 (数学)">平面</a>作为镜子。反射有时被认为是<a href="/wiki/%E5%8F%8D%E6%BC%94" title="反演">圆反演</a>的特殊情情况，参考圆有无限半径。 </p><p>在几何上说，要找到一个点的反射，可从这个点向反射轴画一条<a href="/wiki/%E5%9E%82%E7%BA%BF" class="mw-redirect" title="垂线">垂线</a>。并在另一边延续相同的距离。要找到一个图形的反射，需要反射这个图形的每个点。 </p><p>两次反射回到原来的地方。反射保持在点之间的距离。反射不移动在镜子上的点，镜子的维数比发生反射的空间的维数要小1。这些观察允许我们形式化反射的定义：反射是<a href="/wiki/%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E7%A9%BA%E9%97%B4" title="欧几里得空间">欧几里得空间</a>的<a href="/wiki/%E5%B0%8D%E5%90%88" title="對合">对合</a><a href="/wiki/%E7%AD%89%E8%B7%9D%E5%90%8C%E6%9E%84" title="等距同构">等距同构</a>，它的<a href="/wiki/%E4%B8%8D%E5%8A%A8%E7%82%B9" title="不动点">不动点</a>集合是<a href="/wiki/%E4%BD%99%E7%BB%B4%E6%95%B0" class="mw-redirect" title="余维数">余维数</a>为1的<a href="/wiki/%E4%BB%BF%E5%B0%84%E7%A9%BA%E9%97%B4" title="仿射空间">仿射子空间</a>。 </p><p>在经历特定反射后不改变的图形被称为有<a href="/w/index.php?title=%E5%8F%8D%E5%B0%84%E5%AF%B9%E7%A7%B0%E6%80%A7&action=edit&redlink=1" class="new" title="反射对称性（页面不存在）">反射对称性</a>。 </p><p>密切关联于反射的是<a href="/w/index.php?title=%E6%96%9C%E5%8F%8D%E5%B0%84&action=edit&redlink=1" class="new" title="斜反射（页面不存在）">斜反射</a>和<a href="/wiki/%E5%8F%8D%E6%BC%94" title="反演">圆反演</a>。这些变换仍对合于有余维数1的不动点的集合，但它们不再是等距的。 </p> <div class="mw-heading mw-heading2"><h2 id="豪斯霍尔德变换"><span id=".E8.B1.AA.E6.96.AF.E9.9C.8D.E5.B0.94.E5.BE.B7.E5.8F.98.E6.8D.A2"></span>豪斯霍尔德变换</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)&action=edit&section=1" title="编辑章节：豪斯霍尔德变换"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r85099211">.mw-parser-output .hatnote{font-size:small}.mw-parser-output div.hatnote{padding-left:2em;margin-bottom:0.8em;margin-top:0.8em}.mw-parser-output .hatnote-notice-img::after{content:"\202f \202f \202f \202f "}.mw-parser-output .hatnote-notice-img-small::after{content:"\202f \202f "}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}body.skin-minerva .mw-parser-output .hatnote-notice-img,body.skin-minerva .mw-parser-output .hatnote-notice-img-small{display:none}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">主条目：<a href="/wiki/%E8%B1%AA%E6%96%AF%E9%9C%8D%E5%B0%94%E5%BE%B7%E5%8F%98%E6%8D%A2" title="豪斯霍尔德变换">豪斯霍尔德变换</a></div> <p>给定在<a href="/wiki/%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E7%A9%BA%E9%97%B4" title="欧几里得空间">欧几里得空间</a><b>R</b><sup><i>n</i></sup>中的一个向量<i>a</i>，在通过原点的<a href="/wiki/%E6%AD%A3%E4%BA%A4" title="正交">正交</a>于<i>a</i>的<a href="/wiki/%E8%B6%85%E5%B9%B3%E9%9D%A2" title="超平面">超平面</a>中的反射的公式是 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Ref} _{a}(v)=v-2{\frac {v\cdot a}{a\cdot a}}a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>v</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>v</mi> <mo>−</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>v</mi> <mo>⋅</mo> <mi>a</mi> </mrow> <mrow> <mi>a</mi> <mo>⋅</mo> <mi>a</mi> </mrow> </mfrac> </mrow> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Ref} _{a}(v)=v-2{\frac {v\cdot a}{a\cdot a}}a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59f2c7b1a59fd3070f113340142a06196690c905" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.927ex; height:4.676ex;" alt="{\displaystyle \mathrm {Ref} _{a}(v)=v-2{\frac {v\cdot a}{a\cdot a}}a}"></span></dd></dl> <p>这里的<i>v</i>·<i>a</i>指示<i>v</i>和<i>a</i>的<a href="/wiki/%E7%82%B9%E7%A7%AF" title="点积">点积</a>。注意在上面等式中的第二项就是<i>v</i>在<i>a</i>上的<a href="/wiki/%E6%8A%95%E5%BD%B1" class="mw-disambig" title="投影">投影</a>的两倍。可以轻易的检查 </p> <ul><li>Ref<sub><i>a</i></sub>(<i>v</i>) = − <i>v</i>，如果<i>v</i>平行于<i>a</i>，</li> <li>Ref<sub><i>a</i></sub>(<i>v</i>) = <i>v</i>，如果<i>v</i>垂直于<i>a</i>。</li></ul> <p>因为这些反射是欧几里得空间的固定原点的等距同构，它们可以表示为<a href="/wiki/%E6%AD%A3%E4%BA%A4%E7%9F%A9%E9%98%B5" title="正交矩阵">正交矩阵</a>。对应于上面反射的正交矩阵是有如下元素的矩阵 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R_{ij}=\delta _{ij}-2{\frac {a_{i}a_{j}}{\|a\|^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mi>j</mi> </mrow> </msub> <mo>−</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> </msub> </mrow> <mrow> <mo fence="false" stretchy="false">‖</mo> <mi>a</mi> <msup> <mo fence="false" stretchy="false">‖</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R_{ij}=\delta _{ij}-2{\frac {a_{i}a_{j}}{\|a\|^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e02f41ba26f3864a956f79012e75c5e063b7004" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:18.297ex; height:5.843ex;" alt="{\displaystyle R_{ij}=\delta _{ij}-2{\frac {a_{i}a_{j}}{\|a\|^{2}}}}"></span></dd></dl> <p>这里的δ<sub><i>ij</i></sub>是<a href="/wiki/%E5%85%8B%E7%BD%97%E5%86%85%E5%85%8B%CE%B4" class="mw-redirect" title="克罗内克δ">克罗内克δ</a>。 </p><p>在仿射超平面<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v\cdot a=c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo>⋅</mo> <mi>a</mi> <mo>=</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v\cdot a=c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/153ae5b4c99aa71dfb09e8562194f691d6c0bbcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.142ex; height:1.676ex;" alt="{\displaystyle v\cdot a=c}"></span>中的反射的公式是 </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {Ref} _{a,c}(v)=v-2{\frac {v\cdot a-c}{a\cdot a}}a.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">R</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">f</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>a</mi> <mo>,</mo> <mi>c</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>v</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>v</mi> <mo>−</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>v</mi> <mo>⋅</mo> <mi>a</mi> <mo>−</mo> <mi>c</mi> </mrow> <mrow> <mi>a</mi> <mo>⋅</mo> <mi>a</mi> </mrow> </mfrac> </mrow> <mi>a</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {Ref} _{a,c}(v)=v-2{\frac {v\cdot a-c}{a\cdot a}}a.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3ea8cea87b4d153631e78b8ba2df6ded5603427" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:27.488ex; height:5.009ex;" alt="{\displaystyle \mathrm {Ref} _{a,c}(v)=v-2{\frac {v\cdot a-c}{a\cdot a}}a.}"></span></dd></dl> <p>任何一个<b>R</b><sup><i>n</i></sup>中正交变换都能写成一些反射的<a href="/wiki/%E6%98%A0%E5%B0%84%E7%9A%84%E5%A4%8D%E5%90%88" class="mw-redirect" title="映射的复合">复合</a>，且映射的个数可以不多于<i>n</i>个，这是<a href="/wiki/%E5%98%89%E5%BD%93-%E8%BF%AA%E5%8E%84%E5%A4%9A%E5%86%85%E5%AE%9A%E7%90%86" title="嘉当-迪厄多内定理">嘉当-迪厄多内定理</a>的结论。对于不定空间<b>R</b><sup><i>p,q</i></sup>也是成立的。 </p> <div class="mw-heading mw-heading2"><h2 id="参见"><span id=".E5.8F.82.E8.A7.81"></span>参见</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)&action=edit&section=2" title="编辑章节：参见"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=%E5%9D%90%E6%A0%87%E6%97%8B%E8%BD%AC%E5%92%8C%E5%8F%8D%E5%B0%84&action=edit&redlink=1" class="new" title="坐标旋转和反射（页面不存在）">坐标旋转和反射</a></li> <li><a href="/w/index.php?title=%E5%8F%8D%E5%B0%84%E6%97%8B%E8%BD%AC&action=edit&redlink=1" class="new" title="反射旋转（页面不存在）">反射旋转</a></li> <li><a href="/wiki/%E6%97%8B%E8%BD%AC" title="旋转">旋转</a></li> <li><a href="/wiki/%E5%8F%8D%E6%BC%94" title="反演">反演</a></li> <li><a href="/wiki/%E5%B9%B3%E7%A7%BB" title="平移">平移</a></li> <li><a href="/wiki/%E7%82%B9%E5%8F%8D%E6%BC%94" title="点反演">点反演</a></li> <li><a href="/wiki/%E7%BC%A9%E6%94%BE" title="缩放">缩放</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="外部链接"><span id=".E5.A4.96.E9.83.A8.E9.93.BE.E6.8E.A5"></span>外部链接</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)&action=edit&section=3" title="编辑章节：外部链接"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.cut-the-knot.org/Curriculum/Geometry/Reflection.shtml">Reflection in Line</a>（<a rel="nofollow" class="external text" href="//web.archive.org/web/20070713091423/http://www.cut-the-knot.org/Curriculum/Geometry/Reflection.shtml">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>） at <a href="/wiki/Cut-the-knot" class="mw-redirect" title="Cut-the-knot">cut-the-knot</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">检索自“<a dir="ltr" href="https://zh.wikipedia.org/w/index.php?title=反射_(数学)&oldid=71724386">https://zh.wikipedia.org/w/index.php?title=反射_(数学)&oldid=71724386</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:%E9%A1%B5%E9%9D%A2%E5%88%86%E7%B1%BB" title="Special:页面分类">分类</a>：<ul><li><a href="/wiki/Category:%E5%87%BD%E6%95%B0" title="Category:函数">函数</a></li><li><a href="/wiki/Category:%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E5%AF%B9%E7%A7%B0" title="Category:欧几里得对称">欧几里得对称</a></li><li><a href="/wiki/Category:%E7%BA%BF%E6%80%A7%E7%AE%97%E5%AD%90" title="Category:线性算子">线性算子</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> 本页面最后修订于2022年5月20日 (星期五) 07:20。</li> <li id="footer-info-copyright">本站的全部文字在<a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.zh">知识共享署名-相同方式共享 4.0协议</a>之条款下提供，附加条款亦可能应用。（请参阅<a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">使用条款</a>）<br /> Wikipedia®和维基百科标志是<a rel="nofollow" class="external text" href="https://wikimediafoundation.org/zh">维基媒体基金会</a>的注册商标；维基™是维基媒体基金会的商标。<br /> 维基媒体基金会是按美国国內稅收法501(c)(3)登记的<a class="external text" href="https://donate.wikimedia.org/wiki/Special:MyLanguage/Tax_deductibility">非营利慈善机构</a>。<br /></li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">隐私政策</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:%E5%85%B3%E4%BA%8E">关于维基百科</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:%E5%85%8D%E8%B4%A3%E5%A3%B0%E6%98%8E">免责声明</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">行为准则</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">开发者</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/zh.wikipedia.org">统计</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie声明</a></li> <li id="footer-places-mobileview"><a href="//zh.m.wikipedia.org/w/index.php?title=%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">手机版视图</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-688fc9465-4d8vl","wgBackendResponseTime":222,"wgPageParseReport":{"limitreport":{"cputime":"0.104","walltime":"0.185","ppvisitednodes":{"value":110,"limit":1000000},"postexpandincludesize":{"value":1313,"limit":2097152},"templateargumentsize":{"value":78,"limit":2097152},"expansiondepth":{"value":4,"limit":100},"expensivefunctioncount":{"value":0,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":793,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 85.449 1 -total"," 64.21% 54.863 1 Template:NoteTA"," 32.42% 27.705 1 Template:Main"," 1.69% 1.447 1 Template:Wayback"]},"scribunto":{"limitreport-timeusage":{"value":"0.055","limit":"10.000"},"limitreport-memusage":{"value":884628,"limit":52428800}},"cachereport":{"origin":"mw-api-int.codfw.main-7cb57f8f57-s6hz2","timestamp":"20241125172116","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"\u53cd\u5c04 (\u6570\u5b66)","url":"https:\/\/zh.wikipedia.org\/wiki\/%E5%8F%8D%E5%B0%84_(%E6%95%B0%E5%AD%A6)","sameAs":"http:\/\/www.wikidata.org\/entity\/Q426221","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q426221","author":{"@type":"Organization","name":"\u7ef4\u57fa\u5a92\u4f53\u9879\u76ee\u8d21\u732e\u8005"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2007-06-19T07:09:45Z","dateModified":"2022-05-20T07:20:53Z","image":"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/a\/ae\/Simx2%3DtraslOK.png"}</script> </body> </html>