{"id":8698,"date":"2022-03-01T18:48:33","date_gmt":"2022-03-01T18:48:33","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=8698"},"modified":"2022-03-10T17:48:56","modified_gmt":"2022-03-10T17:48:56","slug":"clase-digital-3-transformaciones-lineales","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-3-transformaciones-lineales\/","title":{"rendered":"Clase digital 3. Transformaciones lineales"},"content":{"rendered":"\n<div class=\"wp-block-cover\" style=\"min-height:284px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"has-background-dim-40 wp-block-cover__gradient-background has-background-dim\"><\/span><img decoding=\"async\" class=\"wp-block-cover__image-background wp-image-8699\" alt=\"text\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/bqlw0ora6f4.jpg\" style=\"object-position:66% 47%\" data-object-fit=\"cover\" data-object-position=\"66% 47%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1200\" class=\"wp-block-cover__image-background wp-image-8699\" alt=\"text\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/bqlw0ora6f4.jpg\" style=\"object-position:66% 47%\" data-object-fit=\"cover\" data-object-position=\"66% 47%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/bqlw0ora6f4.jpg 1600w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/bqlw0ora6f4-300x225.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/bqlw0ora6f4-1024x768.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/bqlw0ora6f4-768x576.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/bqlw0ora6f4-1536x1152.jpg 1536w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><\/noscript><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-base-3-color has-text-color has-large-font-size wp-block-paragraph\">Transformaciones lineales<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"introduccion\">Introducci\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Hola!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Es muy grato tenerte como estudiante en este curso, para mi es un gran honor encontrarme con personas tan disciplinadas y comprometidas con su educaci\u00f3n como lo eres t\u00fa \u00a1Te felicito!&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Volviendo al curso, te invito a proseguir en esta nueva sesi\u00f3n con el tema de Transformaciones Lineales, el cual se dividir\u00e1 en 4 clases que abordar\u00e1n las siguientes tem\u00e1ticas:&nbsp;<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Introducci\u00f3n a las transformaciones lineales.<\/li><li>Propiedades de las transformaciones lineales: n\u00facleo y recorrido.<\/li><li>Transformaciones lineales de R<sup>n<\/sup> hacia R<sup>m<\/sup> y geometr\u00eda de transformaciones de R<sup>2<\/sup> a R<sup>2<\/sup><\/li><li>Matrices de las transformaciones lineales.<\/li><li>Semejanza.<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Iniciaremos nuestro estudio pregunt\u00e1ndonos qu\u00e9 es una transformaci\u00f3n lineal y cu\u00e1l es la funci\u00f3n de una transformaci\u00f3n lineal. Las transformaciones lineales mapean y crean una imagen bajo ciertas reglas que ser\u00e1n tratadas en esta clase.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Una vez que conocemos las im\u00e1genes de los vectores base bajo una transformaci\u00f3n lineal, es posible encontrar las im\u00e1genes de los vectores restantes en el espacio. Esto nos permite enfocarnos en el tratamiento del n\u00facleo y del recorrido de una transformaci\u00f3n lineal y extender nuestro conocimiento del espacio imagen y de la transformaci\u00f3n misma al resto del espacio que ser\u00e1 transformado. Con este conocimiento podemos estudiar las transformaciones lineales de R<sup>n<\/sup> hacia R<sup>m<\/sup> y obtener las propiedades geom\u00e9tricas de las transformaciones lineales de R<sup>2<\/sup> a R<sup>2<\/sup>. Ya que toda transformaci\u00f3n lineal es una transformaci\u00f3n matricial podemos utilizar todo lo aprendido sobre matrices y aplicarlo a las transformaciones lineales usando la matriz est\u00e1ndar. Existen transformaciones lineales de especial inter\u00e9s y que ocurren en el plano como son las rotaciones, reflexiones, expansiones, compresiones, deslizamientos cortantes y las transformaciones inversas de cada una de ellas. Recordemos que todo el aprendizaje del \u00e1lgebra lineal debe de tener como sustento una serie de definiciones y teoremas que respalden nuestro proceder, an\u00e1lisis e interpretaci\u00f3n del resultado y por lo mismo iremos desarrollando la teor\u00eda necesaria sobre cada uno de estos temas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El \u00faltimo tema de nuestro curso es el de <strong>vectores y valores propios<\/strong> e incluye los siguientes subtemas:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Eigenvectores y eigenvalores.<\/li><li>Diagonalizaci\u00f3n.<\/li><li>Diagonalizaci\u00f3n ortogonal; matrices sim\u00e9tricas.<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Este tema tiene gran aplicaci\u00f3n en ciencias y matem\u00e1ticas ya que los eigenvectores son conjuntos de vectores especiales que est\u00e1n asociados con sistemas de ecuaciones lineales y se encuentran en aplicaciones como estabilidad, rotaci\u00f3n y oscilaciones peque\u00f1as de sistemas que vibran.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Demos inicio a esta nuestra tercera y \u00faltima clase digital con mucho \u00e1nimo y nuevamente te invito a reflexionar e investigar sobre las aplicaciones que tienen los temas que abordaremos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Sin m\u00e1s que agregar, comencemos!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"desarrollo-del-tema\">Desarrollo del tema<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">1. Introducci\u00f3n a las transformaciones lineales<\/h3>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.15.24.png\" alt=\"\" class=\"wp-image-8700\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"132\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.15.24.png\" alt=\"\" class=\"wp-image-8700\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.15.24.png 602w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.15.24-300x66.png 300w\" sizes=\"auto, (max-width: 602px) 100vw, 602px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">A las transformaciones lineales que pueden obtener a partir de la multiplicaci\u00f3n por una matriz A se les conoce como transformaciones matriciales y una de este tipo de la rotaci\u00f3n de R2 hasta describir un \u00e1ngulo \u03b8. La transformaci\u00f3n lineal que mapea a un vector v hacia 0, se le conoce como transformaci\u00f3n cero y a la transforma a un vector v hacia \u00e9l mismo se conoce como transformaci\u00f3n identidad. Si lo que realiza la transformaci\u00f3n lineal es mapear el espacio vectorial V hacia s\u00ed mismo (T:V -&gt;V) entonces tendremos un operador lineal sobre V.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Propiedades de las transformaciones lineales: N\u00facleo y recorrido<\/h3>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.18.46.png\" alt=\"\" class=\"wp-image-8701\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"562\" height=\"660\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.18.46.png\" alt=\"\" class=\"wp-image-8701\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.18.46.png 562w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.18.46-255x300.png 255w\" sizes=\"auto, (max-width: 562px) 100vw, 562px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">3. Transformaciones lineales R<sup>n<\/sup> hacia R<sup>m<\/sup>;<sup> <\/sup>Geometr\u00eda de las transformaciones lineales en el plano<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Lo primero que debemos considerar es que toda transformaci\u00f3n lineal de R<sup>n<\/sup> hacia R<sup>m<\/sup> es una transformaci\u00f3n matricial. Si esto es cierto, entonces es posible encontrar una matriz A de mxn tal que T es la multiplicaci\u00f3n por A. Si tienes una base est\u00e1ndar: <strong>e<sub>1<\/sub>, e<sub>2<\/sub>, \u2026, e<sub>n<\/sub><\/strong> para R<sup>n<\/sup>, la matriz A es la matriz de mxn que tiene a T(<strong>e<sub>1<\/sub><\/strong>), T(<strong>e<sub>2<\/sub><\/strong>), \u2026, T(<strong>e<sub>n<\/sub><\/strong>) son sus vectores columna:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.19.37.png\" alt=\"\" class=\"wp-image-8702\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"348\" height=\"109\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.19.37.png\" alt=\"\" class=\"wp-image-8702\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.19.37.png 348w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.19.37-300x94.png 300w\" sizes=\"auto, (max-width: 348px) 100vw, 348px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Tal que:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.19.57.png\" alt=\"\" class=\"wp-image-8703\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"331\" height=\"161\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.19.57.png\" alt=\"\" class=\"wp-image-8703\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.19.57.png 331w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.19.57-300x146.png 300w\" sizes=\"auto, (max-width: 331px) 100vw, 331px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">A esta matriz se le llamar\u00e1 la <strong>matriz est\u00e1ndar<\/strong> para T y cumple con que T(<strong>x<\/strong>)=A<strong>x.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ahora estudiaremos las <strong>transformaciones lineales en el plano<\/strong> y sus propiedades geom\u00e9tricas. Partimos de la matriz est\u00e1ndar dada por:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.20.44.png\" alt=\"\" class=\"wp-image-8704\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"93\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.20.44.png\" alt=\"\" class=\"wp-image-8704\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Entonces:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.21.09.png\" alt=\"\" class=\"wp-image-8705\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"344\" height=\"80\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.21.09.png\" alt=\"\" class=\"wp-image-8705\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.21.09.png 344w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.21.09-300x70.png 300w\" sizes=\"auto, (max-width: 344px) 100vw, 344px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Y esto lo podemos interpretar geom\u00e9tricamente de dos maneras: como vectores o como coordenadas y es aplicable a ambos casos.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Rotaciones:<\/strong> Si T:R2-&gt;R2 hace girar cada punto en el plano alrededor del origen, hasta describir un \u00e1ngulo Q, entonces, se deduce que la matriz est\u00e1ndar para T es:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.21.54.png\" alt=\"\" class=\"wp-image-8706\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"242\" height=\"105\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.21.54.png\" alt=\"\" class=\"wp-image-8706\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Reflexiones:<\/strong> Una reflexi\u00f3n respecto a una recta l que pasa por el origen, es una transformaci\u00f3n que aplica cada punto del plano en su imagen como en un espejo, respecto a la recta l. Son transformaciones lineales y los casos m\u00e1s importantes son las reflexiones respecto a los ejes de coordenadas y respecto a la recta y=x. Las matrices est\u00e1ndar para estas transformaciones son:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.24.19.png\" alt=\"\" class=\"wp-image-8707\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"397\" height=\"307\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.24.19.png\" alt=\"\" class=\"wp-image-8707\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.24.19.png 397w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.24.19-300x232.png 300w\" sizes=\"auto, (max-width: 397px) 100vw, 397px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Expansiones y compresiones:<\/strong> Si la coordenada x de cada punto en el plano se multiplica por una constante positiva k, entonces el efecto es dilatar o comprimir cada figura plana en la direcci\u00f3n x. Si 0&lt;k&lt;1, el resultado es una compresi\u00f3n y si k&gt;1, una expansi\u00f3n. A una expansi\u00f3n de este tipo se le denomina expansi\u00f3n (o compresi\u00f3n) en la direcci\u00f3n x, con el factor k. La matriz est\u00e1ndar para esta transformaci\u00f3n lineal T es:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.25.10.png\" alt=\"\" class=\"wp-image-8708\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"140\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.25.10.png\" alt=\"\" class=\"wp-image-8708\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Esto tambi\u00e9n puede suceder en direcci\u00f3n y, con el factor k, siendo este tipo de transformaciones tambi\u00e9n lineales. En este caso la matriz est\u00e1ndar esta dada por:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.25.33.png\" alt=\"\" class=\"wp-image-8709\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"105\" height=\"89\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.25.33.png\" alt=\"\" class=\"wp-image-8709\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">En la siguiente figura se puede apreciar un ejemplo de cada una de las transformaciones lineales mencionadas.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.26.08.png\" alt=\"\" class=\"wp-image-8710\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"414\" height=\"111\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.26.08.png\" alt=\"\" class=\"wp-image-8710\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.26.08.png 414w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.26.08-300x80.png 300w\" sizes=\"auto, (max-width: 414px) 100vw, 414px\" \/><\/noscript><figcaption>Figura 1. <em>Transformaciones lineales. Howard. 1994.<\/em><\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Deslizamientos cortantes.<\/strong> Un deslizamiento cortante en la direcci\u00f3n x, con factor k, es una transformaci\u00f3n que mueve cada punto (x,y) paralelo al eje x, en una cantidad ky, hacia la posici\u00f3n (x+ky, y). Los puntos que est\u00e1n sobre el eje x no se mueven puesto que y=0. Sin embargo, conforme se avanza alej\u00e1ndose del eje x, la magnitud de y aumenta, por tanto, aquellos puntos m\u00e1s alejados del eje x se mueven una distancia mayor que los que se encuentran m\u00e1s cercanos como se muestra en la figura siguiente:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.28.16.png\" alt=\"\" class=\"wp-image-8711\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"413\" height=\"117\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.28.16.png\" alt=\"\" class=\"wp-image-8711\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.28.16.png 413w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.28.16-300x85.png 300w\" sizes=\"auto, (max-width: 413px) 100vw, 413px\" \/><\/noscript><figcaption>Figura 2. <em>Deslizamientos cortantes. Howard, 1994.<\/em><\/figcaption><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">El deslizamiento cortante tambi\u00e9n puede suceder en direcci\u00f3n y, con factor k moviendo cada punto (x, y) paralelo al eje y, en una cantidad kx, hasta la nueva posici\u00f3n (x, y+kx). Ambos deslizamientos cortantes son transformaciones lineales. La matriz est\u00e1ndar para el deslizamiento cortante en direcci\u00f3n x, con factor k est\u00e1 dado por:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.28.49.png\" alt=\"\" class=\"wp-image-8712\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"137\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.28.49.png\" alt=\"\" class=\"wp-image-8712\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Y de manera an\u00e1loga, la matriz est\u00e1ndar para un deslizamiento cortante en direcci\u00f3n y, de factor k, es&nbsp;<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.29.12.png\" alt=\"\" class=\"wp-image-8713\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"146\" height=\"135\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.29.12.png\" alt=\"\" class=\"wp-image-8713\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Existe la transformaci\u00f3n identidad que mapea cada punto en s\u00ed mismo.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.30.06.png\" alt=\"\" class=\"wp-image-8714\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"579\" height=\"265\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.30.06.png\" alt=\"\" class=\"wp-image-8714\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.30.06.png 579w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.30.06-300x137.png 300w\" sizes=\"auto, (max-width: 579px) 100vw, 579px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">4. Matrices de las transformaciones lineales<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Si tenemos espacios vectoriales V y W con dimensi\u00f3n finita (no necesariamente Rn y Rm), entonces cualquier transformaci\u00f3n lineal T:V-&gt;W se puede considerar como una transformaci\u00f3n matricial. Para esto hay que elegir bases para V y W y trabajar con matrices de coordenadas relativas a estas bases en lugar de con los vectores. Si se eligen las bases B y B\u2019 para V y W, entonces para cada x en V , la matriz de coordenadas [x]B ser\u00e1 un vector en Rn y la matriz de coordenadas [T(x)]B\u2019 ser\u00e1 alg\u00fan vector en Rm. Esta transformaci\u00f3n se puede realizar aplicando la matriz est\u00e1ndar A, para esta transformaci\u00f3n:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.32.44.png\" alt=\"\" class=\"wp-image-8715\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"221\" height=\"72\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.32.44.png\" alt=\"\" class=\"wp-image-8715\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Y consideramos ahora el problema de encontrar una matriz A que satisfaga esta ecuaci\u00f3n. Si suponemos que V es un espacio de n dimensi\u00f3n con base B={u1, u2, \u2026, un} y que W es un espacio de dimensi\u00f3n m con base B\u2019={v1, v2, \u2026,vm}. La matriz que buscamos es de mxn.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.33.30.png\" alt=\"\" class=\"wp-image-8716\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"207\" height=\"119\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.33.30.png\" alt=\"\" class=\"wp-image-8716\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Para todos los vectores x en V. En particular si x es el vector base u1.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.33.50.png\" alt=\"\" class=\"wp-image-8717\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"193\" height=\"50\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.33.50.png\" alt=\"\" class=\"wp-image-8717\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Pero<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.34.09.png\" alt=\"\" class=\"wp-image-8718\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"147\" height=\"175\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.34.09.png\" alt=\"\" class=\"wp-image-8718\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Tal que<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.34.32.png\" alt=\"\" class=\"wp-image-8719\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"314\" height=\"105\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.34.32.png\" alt=\"\" class=\"wp-image-8719\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.34.32.png 314w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.34.32-300x100.png 300w\" sizes=\"auto, (max-width: 314px) 100vw, 314px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Lo que implica que<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.34.50.png\" alt=\"\" class=\"wp-image-8720\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"157\" height=\"112\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.34.50.png\" alt=\"\" class=\"wp-image-8720\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Es decir, la primera columna de A es la matriz de coordenadas para el vector T(u1), con respecto a B\u2019. Lo mismo se hace para x=u2.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.35.16.png\" alt=\"\" class=\"wp-image-8721\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"285\" height=\"463\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.35.16.png\" alt=\"\" class=\"wp-image-8721\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.35.16.png 285w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.35.16-185x300.png 185w\" sizes=\"auto, (max-width: 285px) 100vw, 285px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Es decir, la segunda columna de A es la matriz de coordenadas para el vector T(u2), con respecto a la base B\u2019. As\u00ed podemos encontrar la j-\u00e9sima columna de A y esta es la matriz de coordenadas para el vector T(uj), con respecto a B\u2019. La matriz \u00fanica A que se obtiene se conoce como matriz de T con respecto a las bases B y B\u2019.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.36.02.png\" alt=\"\" class=\"wp-image-8722\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"499\" height=\"76\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.36.02.png\" alt=\"\" class=\"wp-image-8722\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.36.02.png 499w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.36.02-300x46.png 300w\" sizes=\"auto, (max-width: 499px) 100vw, 499px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h3 class=\"wp-block-heading\">5. Semejanza<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">La matriz de un operador lineal T: V-&gt;V depende de la base seleccionada para V. Nosotros siempre buscaremos que la matriz de T sea tan sencilla como se pueda y la obtenemos usando el siguiente teorema.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.36.39.png\" alt=\"\" class=\"wp-image-8723\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"523\" height=\"64\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.36.39.png\" alt=\"\" class=\"wp-image-8723\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.36.39.png 523w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.36.39-300x37.png 300w\" sizes=\"auto, (max-width: 523px) 100vw, 523px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">A\u2019 = P<sup>-1<\/sup> A P<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En donde P es la matriz de transici\u00f3n de B\u2019 a B.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Si tenemos c\u00f3mo se transforma cualquier vector usando T: R2-&gt;R2, usamos los vectores base e1 y e2 y obtenemos A, la matriz est\u00e1ndar para T. Posteriormente encontramos la matriz de transici\u00f3n de B\u2019 hacia B y para eso se necesita la matriz de transici\u00f3n para los vectores B\u2019, con relaci\u00f3n a la base B que es P. Obtenemos la inversa de P y aplicamos el teorema 7 para obtener A\u2019 que es la matriz en relaci\u00f3n a B\u2019.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.37.19.png\" alt=\"\" class=\"wp-image-8724\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"596\" height=\"261\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.37.19.png\" alt=\"\" class=\"wp-image-8724\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.37.19.png 596w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.37.19-300x131.png 300w\" sizes=\"auto, (max-width: 596px) 100vw, 596px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">Eigenvalores y eigenvectores<\/h4>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.37.49.png\" alt=\"\" class=\"wp-image-8725\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"487\" height=\"265\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.37.49.png\" alt=\"\" class=\"wp-image-8725\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.37.49.png 487w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.37.49-300x163.png 300w\" sizes=\"auto, (max-width: 487px) 100vw, 487px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<h4 class=\"wp-block-heading\">Diagonalizaci\u00f3n<\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">Nos enfocamos en dos problemas:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.38.28.png\" alt=\"\" class=\"wp-image-8726\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"471\" height=\"101\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.38.28.png\" alt=\"\" class=\"wp-image-8726\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.38.28.png 471w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.38.28-300x64.png 300w\" sizes=\"auto, (max-width: 471px) 100vw, 471px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Para los cuales se tienen dos planteamientos matriciales:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.38.46.png\" alt=\"\" class=\"wp-image-8727\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"487\" height=\"292\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.38.46.png\" alt=\"\" class=\"wp-image-8727\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.38.46.png 487w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.38.46-300x180.png 300w\" sizes=\"auto, (max-width: 487px) 100vw, 487px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Entonces con base en esto tenemos el siguiente procedimiento:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.39.31.png\" alt=\"\" class=\"wp-image-8728\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"472\" height=\"258\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.39.31.png\" alt=\"\" class=\"wp-image-8728\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.39.31.png 472w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.39.31-300x164.png 300w\" sizes=\"auto, (max-width: 472px) 100vw, 472px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.40.10.png\" alt=\"\" class=\"wp-image-8729\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"407\" height=\"465\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.40.10.png\" alt=\"\" class=\"wp-image-8729\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.40.10.png 407w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.40.10-263x300.png 263w\" sizes=\"auto, (max-width: 407px) 100vw, 407px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El sistema homog\u00e9neo<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.40.40.png\" alt=\"\" class=\"wp-image-8730\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"404\" height=\"301\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.40.40.png\" alt=\"\" class=\"wp-image-8730\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.40.40.png 404w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.40.40-300x224.png 300w\" sizes=\"auto, (max-width: 404px) 100vw, 404px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.42.25.png\" alt=\"\" class=\"wp-image-8731\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"356\" height=\"414\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.42.25.png\" alt=\"\" class=\"wp-image-8731\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.42.25.png 356w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.42.25-258x300.png 258w\" sizes=\"auto, (max-width: 356px) 100vw, 356px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.42.40.png\" alt=\"\" class=\"wp-image-8732\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"344\" height=\"275\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.42.40.png\" alt=\"\" class=\"wp-image-8732\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.42.40.png 344w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.42.40-300x240.png 300w\" sizes=\"auto, (max-width: 344px) 100vw, 344px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.43.10.png\" alt=\"\" class=\"wp-image-8733\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"611\" height=\"448\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.43.10.png\" alt=\"\" class=\"wp-image-8733\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.43.10.png 611w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.43.10-300x220.png 300w\" sizes=\"auto, (max-width: 611px) 100vw, 611px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.43.27.png\" alt=\"\" class=\"wp-image-8734\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"416\" height=\"213\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.43.27.png\" alt=\"\" class=\"wp-image-8734\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.43.27.png 416w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.43.27-300x154.png 300w\" sizes=\"auto, (max-width: 416px) 100vw, 416px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.43.46.png\" alt=\"\" class=\"wp-image-8735\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"385\" height=\"332\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.43.46.png\" alt=\"\" class=\"wp-image-8735\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.43.46.png 385w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.43.46-300x259.png 300w\" sizes=\"auto, (max-width: 385px) 100vw, 385px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.44.05.png\" alt=\"\" class=\"wp-image-8736\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"387\" height=\"343\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.44.05.png\" alt=\"\" class=\"wp-image-8736\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.44.05.png 387w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.44.05-300x266.png 300w\" sizes=\"auto, (max-width: 387px) 100vw, 387px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.44.40.png\" alt=\"\" class=\"wp-image-8737\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"414\" height=\"591\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.44.40.png\" alt=\"\" class=\"wp-image-8737\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.44.40.png 414w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.44.40-210x300.png 210w\" sizes=\"auto, (max-width: 414px) 100vw, 414px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.45.12.png\" alt=\"\" class=\"wp-image-8739\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"346\" height=\"390\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.45.12.png\" alt=\"\" class=\"wp-image-8739\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.45.12.png 346w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.45.12-266x300.png 266w\" sizes=\"auto, (max-width: 346px) 100vw, 346px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.45.36.png\" alt=\"\" class=\"wp-image-8740\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"382\" height=\"424\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.45.36.png\" alt=\"\" class=\"wp-image-8740\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.45.36.png 382w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.45.36-270x300.png 270w\" sizes=\"auto, (max-width: 382px) 100vw, 382px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.45.53.png\" alt=\"\" class=\"wp-image-8742\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"385\" height=\"576\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.45.53.png\" alt=\"\" class=\"wp-image-8742\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.45.53.png 385w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.45.53-201x300.png 201w\" sizes=\"auto, (max-width: 385px) 100vw, 385px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo: Eigenvalores y eigenvectores.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.46.16.png\" alt=\"\" class=\"wp-image-8743\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"342\" height=\"170\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.46.16.png\" alt=\"\" class=\"wp-image-8743\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.46.16.png 342w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.46.16-300x149.png 300w\" sizes=\"auto, (max-width: 342px) 100vw, 342px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.46.45.png\" alt=\"\" class=\"wp-image-8745\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"375\" height=\"339\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.46.45.png\" alt=\"\" class=\"wp-image-8745\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.46.45.png 375w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.46.45-300x271.png 300w\" sizes=\"auto, (max-width: 375px) 100vw, 375px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.47.06.png\" alt=\"\" class=\"wp-image-8746\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"413\" height=\"207\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.47.06.png\" alt=\"\" class=\"wp-image-8746\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.47.06.png 413w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.47.06-300x150.png 300w\" sizes=\"auto, (max-width: 413px) 100vw, 413px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.47.33.png\" alt=\"\" class=\"wp-image-8748\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"503\" height=\"682\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.47.33.png\" alt=\"\" class=\"wp-image-8748\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.47.33.png 503w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.47.33-221x300.png 221w\" sizes=\"auto, (max-width: 503px) 100vw, 503px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Ejemplo:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.47.51.png\" alt=\"\" class=\"wp-image-8750\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"280\" height=\"688\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.47.51.png\" alt=\"\" class=\"wp-image-8750\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.47.51.png 280w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2022\/03\/Captura-de-Pantalla-2022-03-01-a-las-12.47.51-122x300.png 122w\" sizes=\"auto, (max-width: 280px) 100vw, 280px\" \/><\/noscript><\/figure><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">Te invito a revisar los siguientes recursos digitales:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><a href=\"https:\/\/youtu.be\/z0mlihGcuCg\">Introducci\u00f3n a la independencia lineal<\/a><\/li><li><a href=\"https:\/\/youtu.be\/9FpfAxaJlQI\">M\u00e1s sobre independencia lineal<\/a><\/li><li><a href=\"https:\/\/youtu.be\/cOSh0SeMFHE\">Espacios vectoriales generados y ejemplos de independencia lineal<\/a><\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Para concluir, en esta clase digital estudiamos las transformaciones lineales y el tema de eigenvalores y eigenvectores. Las aplicaciones de estos temas son muy variadas y se usan pr\u00e1cticamente en todas las aplicaciones digitales de tu dispositivo m\u00f3vil y computadoras.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Has concluido la \u00faltima clase del curso! \u00a1Muchas felicidades! Ha sido un gozo compartir contigo este trayecto formativo. Deseo que el curso haya cumplido con tus expectativas y encuentres satisfacci\u00f3n con los temas abordados, as\u00ed como con tu desempe\u00f1o y compromiso. No olvides realizar la tarea asignada para la plena conclusi\u00f3n del curso. Espero encontrarte nuevamente, \u00a1hasta pronto!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"fuentes-de-informacion\">Fuentes de informaci\u00f3n<\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li>Howard, A. (1994). Introducci\u00f3n al \u00e1lgebra lineal. (3<sup>a<\/sup> ed.). limusa.<\/li><li>Stanley, I., Grossman, S., &amp; Flores Godoy, J. J. (2019). \u00c1lgebra Lineal. (8\u00aa ed.). McGraw-Hill Interamericana.<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n \u00a1Hola! Es muy grato tenerte como estudiante en este curso, para mi es un gran honor encontrarme con personas tan disciplinadas y comprometidas con su educaci\u00f3n como lo eres t\u00fa \u00a1Te felicito!&nbsp; Volviendo al curso, te invito a proseguir en esta nueva sesi\u00f3n con el tema de Transformaciones Lineales, el cual se dividir\u00e1 en &#8230; <a title=\"Clase digital 3. Transformaciones lineales\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-3-transformaciones-lineales\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 3. Transformaciones lineales\">Leer m\u00e1s<\/a><\/p>\n","protected":false},"author":142,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","episode_type":"","audio_file":"","podmotor_file_id":"","podmotor_episode_id":"","cover_image":"","cover_image_id":"","duration":"","filesize":"","filesize_raw":"","date_recorded":"","explicit":"","block":"","itunes_episode_number":"","itunes_title":"","itunes_season_number":"","itunes_episode_type":"","footnotes":""},"categories":[238,266],"tags":[268,41,267],"class_list":["post-8698","post","type-post","status-publish","format-standard","hentry","category-licenciatura-en-ingenieria-quimica","category-uda-algebra-lineal-licenciatura-en-ingenieria-quimica","tag-carlos-alanias-rodriguez-rico","tag-clase-digital","tag-neli04035-1"],"acf":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/8698","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/users\/142"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/comments?post=8698"}],"version-history":[{"count":4,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/8698\/revisions"}],"predecessor-version":[{"id":8938,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/8698\/revisions\/8938"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=8698"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=8698"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=8698"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}