{"id":175,"date":"2018-01-12T09:06:00","date_gmt":"2018-01-12T08:06:00","guid":{"rendered":"http:\/\/clases.jesussoto.es\/?p=175"},"modified":"2018-01-12T09:06:00","modified_gmt":"2018-01-12T08:06:00","slug":"alg-complemento-ortogonal","status":"publish","type":"post","link":"https:\/\/curso17.jesussoto.es\/?p=175","title":{"rendered":"ALG: Complemento ortogonal"},"content":{"rendered":"<p>En el d\u00eda de hoy hemos trabajado con el complemento ortogonal. Si tenemos un espacio vectorial eucl\u00eddeo de dimensi\u00f3n finita, $E$, definimos el complemento ortogonal (a veces simplemente ortogonal) de un subespacio $S$ de $E$ a $$S^\\bot=\\{\\vec{v}\\in E|\\;&lt;\\vec{v},\\vec{u}&gt;=0\\,\\forall \\vec{u}\\in S\\}$$<\/p>\n<p>El ortogonal de un conjunto cumple propiedades muy interesantes, como que es un subespacio vectorial, y cuando $S$ es un subespacio vectorial entonces $$E=S\\oplus S^{\\bot}$$<\/p>\n<p>Esto implica que para todo vector $\\vec{v}\\in E$ existir\u00e1n dos \u00fanicos vectores $\\vec{u}\\in S$ y $\\vec{w}\\in S^{\\bot}$, tales que $$\\vec{v}=\\vec{u}+\\vec{w}.$$<\/p>\n<table id=\"yzpi\" width=\"100%\" border=\"0\" cellspacing=\"0\" cellpadding=\"3\" bgcolor=\"#999999\">\n<tbody>\n<tr>\n<td width=\"100%\"><strong>Ejercicio:<\/strong> Hallar el complemento ortogonal del subespacio dado por las ecuaciones impl\u00edcitas $\\pi=\\{(x,y,z,t,u)|x+y-t=0,x-z-u=0\\}$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>En el d\u00eda de hoy hemos trabajado con el complemento ortogonal. Si tenemos un espacio vectorial eucl\u00eddeo de dimensi\u00f3n finita, $E$, definimos el complemento ortogonal (a veces simplemente ortogonal) de un subespacio $S$ de $E$ a $$S^\\bot=\\{\\vec{v}\\in E|\\;&lt;\\vec{v},\\vec{u}&gt;=0\\,\\forall \\vec{u}\\in S\\}$$ El ortogonal de un conjunto cumple propiedades muy interesantes, como que es un subespacio vectorial,&hellip; <a class=\"more-link\" href=\"https:\/\/curso17.jesussoto.es\/?p=175\">Seguir leyendo <span class=\"screen-reader-text\">ALG: Complemento ortogonal<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[4],"tags":[],"_links":{"self":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/175"}],"collection":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=175"}],"version-history":[{"count":1,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/175\/revisions"}],"predecessor-version":[{"id":176,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/175\/revisions\/176"}],"wp:attachment":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=175"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=175"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=175"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}