{"id":189,"date":"2018-01-19T09:13:49","date_gmt":"2018-01-19T08:13:49","guid":{"rendered":"http:\/\/clases.jesussoto.es\/?p=189"},"modified":"2018-01-19T09:13:49","modified_gmt":"2018-01-19T08:13:49","slug":"alg-autovectores-y-autovalores","status":"publish","type":"post","link":"https:\/\/curso17.jesussoto.es\/?p=189","title":{"rendered":"ALG: Autovectores y autovalores"},"content":{"rendered":"

Comenzamos explicado que son los valores y vectores propios, o autovalores y autovectores, de una matriz y.<\/p>\n

Hemos aprendido a calcular los autovalores de una matriz cuadrada. Recordad que para nuestro prop\u00f3sito necesitamos encontrar las soluciones de la ecuaci\u00f3n que plantea el determinante $$det(A-\\lambda\\, I),$$ siendo $A\\in\\mathcal{C}_n(\\mathbb{K})$, donde $\\mathbb{K}$ es $\\mathbb{R} \u00f3 \\mathbb{C}$, la matriz cuadrada y $I$ la indentidad en $\\mathcal{C}_n(\\mathbb{K})$.<\/p>\n

El polinomio p(\u03bb) = det(A \u2013 \u03bbI) es el polinomio caracter\u00edstico de A: los valores propios de una matriz son los ceros de su polinomio caracter\u00edstico (soluciones de la ecuaci\u00f3n caracter\u00edstica).<\/p>\n

 <\/p>\n\n\n\n
Ejercicio:<\/strong> Calcular los valores propios de la matriz real $$\\begin{bmatrix}0 & 1 & -1 \\\\ 1 & 1 & 0 \\\\ -1 & 0 & 1 \\end{bmatrix}$$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Comenzamos explicado que son los valores y vectores propios, o autovalores y autovectores, de una matriz y. Hemos aprendido a calcular los autovalores de una matriz cuadrada. Recordad que para nuestro prop\u00f3sito necesitamos encontrar las soluciones de la ecuaci\u00f3n que plantea el determinante $$det(A-\\lambda\\, I),$$ siendo $A\\in\\mathcal{C}_n(\\mathbb{K})$, donde $\\mathbb{K}$ es $\\mathbb{R} \u00f3 \\mathbb{C}$, la matriz… Seguir leyendo ALG: Autovectores y autovalores<\/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\/189"}],"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=189"}],"version-history":[{"count":1,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/189\/revisions"}],"predecessor-version":[{"id":190,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/189\/revisions\/190"}],"wp:attachment":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=189"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=189"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=189"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}