{"id":34867,"date":"2025-01-14T10:40:08","date_gmt":"2025-01-14T08:40:08","guid":{"rendered":"https:\/\/www.cpge-brizeux.fr\/wordpress\/?p=34867"},"modified":"2025-01-17T14:45:31","modified_gmt":"2025-01-17T12:45:31","slug":"34867","status":"publish","type":"post","link":"https:\/\/www.cpge-brizeux.fr\/wordpress\/pc\/mathematiques-pc-2425\/34867.html","title":{"rendered":"Semaine 16 du  13\/01 au 17\/01"},"content":{"rendered":"<div style=\"border: 2px solid; border-radius: 6px; color: #dc143c; padding-top: 1px; padding-bottom: 1px; padding-left: 20px; margin: 1px;\">\n<p><b><big><span style=\"color: #dc143c;\">Programme de colles de la semaine du 20\/01 au 24\/01 : <a href=\"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-content\/uploads\/16_prog_iparam_eucl.pdf\">16_prog_iparam_eucl<\/a><br \/>\n<\/span><\/big><\/b><\/p>\n<\/div>\n<div style=\"border: 2px solid; border-radius: 6px; color: #00008b; padding-top: 1px; padding-bottom: 1px; padding-left: 20px; margin: 1px;\">\n<p><span style=\"text-decoration: underline; color: #000000;\"><span style=\"font-size: 18pt;\"><strong>Chapitre X Isom\u00e9tries des espaces euclidiens<br \/>\n<\/strong><\/span><\/span><\/p>\n<p><span style=\"color: #000000;\">Rappels de PCSI : produits scalaires, espaces euclidien. Norme euclidienne, distance euclidienne. Base orthonormale. Th\u00e9or\u00e8me de projection sur un sous-espace vectoriel muni d&rsquo;une base orthonorm\u00e9e; Algorithme de Gram-Schmidt.Orthogonal d&rsquo;un s.-e.v., somme directe, cas de la dimension finie. Isom\u00e9tries.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #000000;\"><em>exercice(s) : 1<br \/>\n<\/em><\/span><\/p>\n<hr \/>\n<p><span style=\"color: #000000;\">Isom\u00e9tries et bases orthonorm\u00e9es. Propri\u00e9t\u00e9s des isom\u00e9tries.<br \/>\n<\/span><\/p>\n<p><span style=\"color: #000000;\">exercice(s) : 2<br \/>\n<\/span><\/p>\n<hr \/>\n<p><span style=\"color: #000000;\">Matrices orthogonales. Groupe orthogonal, groupe sp\u00e9cial orthogonal.<\/span><\/p>\n<p><span style=\"color: #000000;\">exercice(s) : 5, 13<br \/>\n<\/span><\/p>\n<hr \/>\n<p><span style=\"color: #000000;\">Stabilit\u00e9 d&rsquo;un se v par une isom\u00e9trie, de son orthogonal<br \/>\n<\/span><\/p>\n<p><span style=\"color: #000000;\">exercice(s) : 15, 3,4,7<br \/>\n<\/span><\/p>\n<\/div>\n<div style=\"border: 2px solid; border-radius: 6px; color: #2e8b57; padding-top: 1px; padding-bottom: 1px; padding-left: 20px; margin: 1px;\">\n<p><span style=\"font-size: 12pt;\">Notes de cours : <a href=\"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-content\/uploads\/ch10_eucl_auto-adjoints.pdf\">ch10_eucl_auto-adjoints<\/a><br \/>\n<\/span><\/p>\n<p><span style=\"font-size: 12pt;\"><b><big><span style=\"color: #2e8b57;\">Documents distribu\u00e9s : <\/span><\/big><\/b><\/span><b><big><span style=\"color: #2e8b57;\"><span style=\"font-size: 12pt;\">TD : <a href=\"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-content\/uploads\/td10_eucl_auto-adjoints.pdf\">td10_eucl_auto-adjoints<\/a><br \/>\n<\/span><\/span><\/big><\/b><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Programme de colles de la semaine du 20\/01 au 24\/01 : 16_prog_iparam_eucl Chapitre X Isom\u00e9tries des espaces euclidiens Rappels de PCSI : produits scalaires, espaces euclidien. Norme euclidienne, distance euclidienne. Base orthonormale. Th\u00e9or\u00e8me de projection sur un sous-espace vectoriel muni&hellip;<\/p>\n<p class=\"more-link-p\"><a class=\"more-link\" href=\"https:\/\/www.cpge-brizeux.fr\/wordpress\/pc\/mathematiques-pc-2425\/34867.html\">Read more &rarr;<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[386],"tags":[],"class_list":["post-34867","post","type-post","status-publish","format-standard","hentry","category-mathematiques-pc-2425"],"_links":{"self":[{"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/posts\/34867","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/users\/9"}],"replies":[{"embeddable":true,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/comments?post=34867"}],"version-history":[{"count":5,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/posts\/34867\/revisions"}],"predecessor-version":[{"id":34907,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/posts\/34867\/revisions\/34907"}],"wp:attachment":[{"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/media?parent=34867"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/categories?post=34867"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.cpge-brizeux.fr\/wordpress\/wp-json\/wp\/v2\/tags?post=34867"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}