{"id":61240,"date":"2007-08-11T00:00:00","date_gmt":"2007-08-11T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/analisis-de-la-perturbacion-de-matrices-elementos-en-anillos-y-operadores\/"},"modified":"2007-08-11T00:00:00","modified_gmt":"2007-08-11T00:00:00","slug":"analisis-de-la-perturbacion-de-matrices-elementos-en-anillos-y-operadores","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/teoria-de-matrices\/analisis-de-la-perturbacion-de-matrices-elementos-en-anillos-y-operadores\/","title":{"rendered":"Analisis de la perturbacion de matrices, elementos en anillos y operadores"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Jos\u00e9 Ignacio V\u00e9lez Cerrada <\/strong><\/h2>\n<p>Este trabajo se centra en el estudio de la perturbaci\u00f3n de la inversa de drazin, de aplicaci\u00f3n en diversos problemas de ciencia  e ingenier\u00eda  (resoluci\u00f3n de sistemas lineales, ecuaciones diferenciales, ecuaciones en diferencias,  criptograf\u00eda, teor\u00eda del control \u00f3ptimo, cadenas de  markov, etc.). en 1958, m. P. Drazin introdujo la \u00abpseudoinversa\u00bb llamada inversa de drazin. Esta inversa es inestable bajo perturbaciones. S. L. Campbell y c. D. Meyer, establecieron una condici\u00f3n necesaria y sufciente para la continuidad de la inversa de drazin. La obtenci\u00f3n de cotas expl\u00edcitas de car\u00e1cter general de la perturbaci\u00f3n de la inversa de drazin y de su error relativo es un problema complejo y a\u00fan abierto, que ha sido abordado por investigadores en el tema bajo ciertas condiciones sobre la matriz perturbaci\u00f3n.  en el contexto de las matrices cuadradas se estudia la perturbaci\u00f3n de la proyecci\u00f3n espectral asociada al 0 en relaci\u00f3n con la inversa de drazin. Tambi\u00e9n, dada una matriz a, se analizan aquellas matrices perturbaci\u00f3n b relacionadas con a por condiciones dadas en t\u00e9rminos de sus proyecciones espectrales.  se introduce la clase cs de las matrices perturbaci\u00f3n b que satisfacen condiciones que involucran a las im\u00e1genes y n\u00facleos de las matrices a y b elevadas a sus respectivos \u00edndices de drazin, donde a es una matriz fijada de antemano. se prueba que las condiciones que definen la clase cs son equivalentes a otras dadas en t\u00e9rminos de los rangos de las matrices a y b elevadas a sus correspondientes \u00edndices, incluyendo a la establecida por campbell y meyer, y que la clase cs puede ser descrita en t\u00e9rminos de las proyecciones espectrales. tanto para las matrices con proyecciones espectrales relacionadas como para aquellas que pertenecen a cs se dan diversas caracterizaciones de la perturbaci\u00f3n, su inversa de drazin y proyecci\u00f3n espectral. De estas caracterizaciones se derivan cotas superiores de  la inversa de drazin de la perturbaci\u00f3n, d<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Analisis de la perturbacion de matrices, elementos en anillos y operadores<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Analisis de la perturbacion de matrices, elementos en anillos y operadores <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Jos\u00e9 Ignacio V\u00e9lez Cerrada <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Polit\u00e9cnica de Madrid<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 08\/11\/2007<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>B. Nieves Castro  Gonz\u00e1lez<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Emilio Torrrano Gim\u00e9nez <\/li>\n<li>Froilan Martinez Dopico (vocal)<\/li>\n<li>N\u00e9stor Javier Thome Coppo (vocal)<\/li>\n<li>Jos\u00e9 Esteban Gal\u00e9 Gimeno (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Jos\u00e9 Ignacio V\u00e9lez Cerrada Este trabajo se centra en el estudio de la perturbaci\u00f3n de la inversa [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[10643,12792,26350,16008,8246],"tags":[135287,135288,135289,135291,135286,135290],"class_list":["post-61240","post","type-post","status-publish","format-standard","hentry","category-algebra-de-operadores","category-algebra-lineal","category-matrices","category-politecnica-de-madrid","category-teoria-de-matrices","tag-b-nieves-castro-gonzalez","tag-emilio-torrrano-gimenez","tag-froilan-Martinez-dopico","tag-jose-esteban-gale-gimeno","tag-jose-ignacio-velez-cerrada","tag-nestor-javier-thome-coppo"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/61240","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=61240"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/61240\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=61240"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=61240"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=61240"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}