{"id":145,"date":"2017-12-18T11:48:43","date_gmt":"2017-12-18T10:48:43","guid":{"rendered":"http:\/\/clases.jesussoto.es\/?p=145"},"modified":"2017-12-19T11:52:38","modified_gmt":"2017-12-19T10:52:38","slug":"efm-sistemas-con-autovalores-complejos","status":"publish","type":"post","link":"https:\/\/curso17.jesussoto.es\/?p=145","title":{"rendered":"EFM: Sistemas con autovalores complejos"},"content":{"rendered":"<p>Por \u00faltimo tenemos que la soluci\u00f3n de $p_A(\\lambda)=0$ sea compleja; es decir, $\\lambda=\\alpha\\pm \\beta i$, en ese caso la soluci\u00f3n general ser\u00e1 de la forma<br \/>\n$$X=c_1\\vec{v}e^{\\lambda t}+c_2\\bar{\\vec{v}}e^{\\bar{\\lambda} t},$$ donde $\\bar{\\lambda}$ es el conjugado de $\\lambda$ y $\\bar{\\vec{v}}$ es el vector conjugado del vector propio $\\vec{v}$. Esta forma tambi\u00e9n se puede expresar utilizando los senos y cosenos.<\/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> Resolver el sistema de ED $$X&#8217;=\\begin{pmatrix}<br \/>\n1 &#038; 1\\\\<br \/>\n4 &#038; 1\\\\<br \/>\n\\end{pmatrix}X$$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Por \u00faltimo tenemos que la soluci\u00f3n de $p_A(\\lambda)=0$ sea compleja; es decir, $\\lambda=\\alpha\\pm \\beta i$, en ese caso la soluci\u00f3n general ser\u00e1 de la forma $$X=c_1\\vec{v}e^{\\lambda t}+c_2\\bar{\\vec{v}}e^{\\bar{\\lambda} t},$$ donde $\\bar{\\lambda}$ es el conjugado de $\\lambda$ y $\\bar{\\vec{v}}$ es el vector conjugado del vector propio $\\vec{v}$. Esta forma tambi\u00e9n se puede expresar utilizando los senos y&hellip; <a class=\"more-link\" href=\"https:\/\/curso17.jesussoto.es\/?p=145\">Seguir leyendo <span class=\"screen-reader-text\">EFM: Sistemas con autovalores complejos<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/145"}],"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=145"}],"version-history":[{"count":1,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/145\/revisions"}],"predecessor-version":[{"id":148,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/145\/revisions\/148"}],"wp:attachment":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=145"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=145"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}