{"id":247,"date":"2021-06-01T18:52:30","date_gmt":"2021-06-01T16:52:30","guid":{"rendered":"http:\/\/matimatheque.fr\/?page_id=247"},"modified":"2023-08-21T17:14:20","modified_gmt":"2023-08-21T15:14:20","slug":"algebre-2a","status":"publish","type":"page","link":"https:\/\/matimatheque.fr\/?page_id=247","title":{"rendered":"Alg\u00e8bre"},"content":{"rendered":"\n

Espaces vectoriels 1A<\/h2>\n\n\n
\n\n\n\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
polycop<\/a><\/td><\/td><\/td>\n<\/tr>\n
<\/td>R005<\/a><\/td>d\u00e9finitions, r\u00e8gles de calcul sev<\/em><\/td>\n<\/tr>\n
<\/td>R005bis<\/a><\/td> sous-espace vectoriel<\/em><\/td>\n<\/tr>\n
<\/td>R006<\/a><\/td> somme de 2 sev<\/em><\/td>\n<\/tr>\n
<\/td>R007<\/a><\/td>familles g\u00e9n\u00e9ratrices<\/em><\/td>\n<\/tr>\n
<\/td>R008<\/a><\/td>familles libres ou li\u00e9es<\/em><\/td>\n<\/tr>\n
<\/td>R009<\/a><\/td>bases<\/em><\/td>\n<\/tr>\n
<\/td>R010<\/a><\/td>ev de dim finie<\/em><\/td>\n<\/tr>\n
bases<\/td>exos<\/a><\/td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n<\/div>\n\n\n\n

Applications lin\u00e9aires 1A<\/h2>\n\n\n
\n\n\n\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
polycop<\/a><\/td><\/td><\/td>\n<\/tr>\n
<\/td>R001<\/a><\/td>premi\u00e8res d\u00e9finitions<\/em><\/td>\n<\/tr>\n
<\/td>R002<\/a><\/td>noyau et image<\/em><\/td>\n<\/tr>\n
<\/td>R003<\/a><\/td>\u00e9quations lin\u00e9aires<\/em><\/td>\n<\/tr>\n
<\/td>R004<\/a><\/td>app.lin. d\u00e9finies sur un sev de dim finie(1\/3)<\/em><\/td>\n<\/tr>\n
<\/td>R004bis<\/a><\/td>app.lin. d\u00e9finies sur un sev de dim finie(2\/3)<\/em><\/td>\n<\/tr>\n
<\/td>R004ter<\/a><\/td>app.lin. d\u00e9finies sur un sev de dim finie(3\/3)<\/em><\/td>\n<\/tr>\n
application lin\u00e9aire<\/td>exos<\/a><\/td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n<\/div>\n\n\n\n

Matrices 1A<\/h2>\n\n\n
\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
<\/td><\/td><\/td>\n<\/tr>\n<\/thead>\n
polycop<\/a><\/td><\/td><\/td>\n<\/tr>\n
<\/td>R011<\/a><\/td>d\u00e9finitions<\/em><\/td>\n<\/tr>\n
<\/td>R012<\/a><\/td>l 'espace vectoriel des matrices<\/em><\/td>\n<\/tr>\n
<\/td>R013<\/a><\/td>produit matriciel<\/em><\/td>\n<\/tr>\n
<\/td>R014<\/a><\/td>transposition<\/em><\/td>\n<\/tr>\n
<\/td>R015<\/a><\/td> matrices diagonales et triangulaires<\/em><\/td>\n<\/tr>\n
<\/td>R016<\/a><\/td>matrices inversibles(1\/2)<\/em><\/td>\n<\/tr>\n
<\/td>R016bis<\/a><\/td>matrices inversibles(2\/2)<\/em><\/td>\n<\/tr>\n
<\/td>R017<\/a><\/td>application canoniquement associ\u00e9<\/em><\/td>\n<\/tr>\n
<\/td>R018<\/a><\/td>propri\u00e9t\u00e9s du rang<\/em><\/td>\n<\/tr>\n
<\/td>R019<\/a><\/td>caract\u00e9risations des matrices inversibles<\/em><\/td>\n<\/tr>\n
<\/td>R020<\/a><\/td>formules de changement de bases<\/em><\/td>\n<\/tr>\n
<\/td>V010<\/a><\/td>matrices semblables(1\/3)<\/em><\/td>\n<\/tr>\n
<\/td>V011<\/a><\/td>matrices semblables(2\/3)<\/em><\/td>\n<\/tr>\n
<\/td>V012<\/a><\/td>matrices semblables(3\/3)<\/em><\/td>\n<\/tr>\n
matrices<\/td>exos<\/a><\/td><\/td>\n<\/tr>\n
syst\u00e8mes lin\u00e9aires<\/td>exos<\/a><\/td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n<\/div>\n\n\n\n

Compl\u00e9ments d’alg\u00e8bre lin\u00e9aire 2A<\/h2>\n\n\n
\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
<\/td><\/td><\/td>\n<\/tr>\n<\/thead>\n
projecteurs & sym\u00e9tries<\/a><\/td>R030<\/a><\/td>homoth\u00e9ties<\/em><\/td>\n<\/tr>\n
<\/td>R031<\/a><\/td>projections (1\/4)<\/em><\/td>\n<\/tr>\n
<\/td>R032<\/a><\/td>projections (2\/4)<\/em><\/td>\n<\/tr>\n
<\/td>R033<\/a><\/td>projections (3\/4)<\/em><\/td>\n<\/tr>\n
<\/td>R034<\/a><\/td>projections (4\/4)<\/em><\/td>\n<\/tr>\n
<\/td>R035<\/a><\/td>sym\u00e9tries vectorielles (1\/3)<\/em><\/td>\n<\/tr>\n
<\/td>R036<\/a><\/td>sym\u00e9tries vectorielles (2\/3)<\/em><\/td>\n<\/tr>\n
<\/td>R037<\/a><\/td>sym\u00e9tries vectorielles (3\/3)<\/em><\/td>\n<\/tr>\n
trace, hyperplans et formes lin\u00e9aires<\/a><\/td><\/td>hyperplan et forme lin\u00e9aire<\/em><\/td>\n<\/tr>\n
<\/td>A001<\/a><\/td>intersection d'hyperplans<\/em><\/td>\n<\/tr>\n
<\/td>R040<\/a><\/td>trace d'une matrice<\/em><\/td>\n<\/tr>\n
<\/td>R041<\/a><\/td>trace d'un endomorphisme<\/em><\/td>\n<\/tr>\n
d\u00e9terminants<\/a><\/td>V016<\/a><\/td>d\u00e9terminant d'une matrice<\/em><\/td>\n<\/tr>\n
<\/td>V018<\/a><\/td>d\u00e9terminant d'une famille de vecteurs<\/em><\/td>\n<\/tr>\n
<\/td>V017<\/a><\/td>d\u00e9terminant d'un endomorphisme<\/em><\/td>\n<\/tr>\n
<\/td><\/td>syst\u00e8me lin\u00e9aire et matrice<\/em><\/td>\n<\/tr>\n
compl\u00e9ments AL<\/a><\/td><\/td>sev engendr\u00e9 par une partie<\/em><\/td>\n<\/tr>\n
<\/td>W009<\/a><\/td>somme de n sev<\/em><\/td>\n<\/tr>\n
<\/td>W010<\/a><\/td> projecteurs associ\u00e9s \u00e0 une d\u00e9composition<\/em><\/td>\n<\/tr>\n
<\/td>W012<\/a><\/td>famille quelconque de vecteurs<\/em><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n<\/div>\n\n\n\n

R\u00e9duction 2A<\/h2>\n\n\n
\n\n\n\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
\u00e9l\u00e9ments propres<\/a><\/td>V037<\/a><\/td>polyn\u00f4me caract\u00e9ristique d'une matrice<\/em><\/td>\n<\/tr>\n
<\/td>V040<\/a><\/td>polyn\u00f4me caract\u00e9ristique d'un endomorphisme<\/em><\/td>\n<\/tr>\n
<\/td>V060<\/a><\/td>\u00e9l\u00e9ments propres d'un endomorphisme 1<\/em><\/td>\n<\/tr>\n
<\/td>V061<\/a><\/td>\u00e9l\u00e9ments propres d'un endomorphisme 2<\/em><\/td>\n<\/tr>\n
<\/td>V062<\/a><\/td>\u00e9l\u00e9ments propres d'une matrice<\/em><\/td>\n<\/tr>\n
<\/td>V063<\/a><\/td>propri\u00e9t\u00e9s des \u00e9l\u00e9ments propres<\/em><\/td>\n<\/tr>\n
<\/td><\/td>rappels sur les polyn\u00f4mes<\/em><\/td>\n<\/tr>\n
<\/td>V032<\/a><\/td>polyn\u00f4me matriciel<\/em><\/td>\n<\/tr>\n
<\/td>V033<\/a><\/td>polyn\u00f4me d'endomorphisme<\/em><\/td>\n<\/tr>\n
<\/td><\/td>compl\u00e9ment: matrice r\u00e9elle vue comme complexe<\/em><\/td>\n<\/tr>\n
<\/td>V034<\/a><\/td>calcul de A^n par polyn\u00f4me annulateur<\/em><\/td>\n<\/tr>\n
\u00e9l\u00e9ments propres<\/em><\/td>exos<\/a><\/td><\/td>\n<\/tr>\n
<\/td><\/td><\/td>\n<\/tr>\n
r\u00e9duction<\/a><\/td>W008<\/a><\/td>sev stable, endomorphisme enduit<\/em><\/td>\n<\/tr>\n
<\/td>V041<\/a><\/td>endomorphismes diagonalisables 1<\/em><\/td>\n<\/tr>\n
<\/td>V064<\/a><\/td>endomorphismes diagonalisables 2 <\/em>
\n<\/td>\n<\/tr>\n
<\/td>V065<\/a><\/td>matrices diagonalisables 1<\/em><\/td>\n<\/tr>\n
<\/td>V066<\/a><\/td>matrices diagonalisables 2<\/em><\/td>\n<\/tr>\n
<\/td>V043<\/a><\/td>endomorphismes trigonalisables<\/em><\/td>\n<\/tr>\n
<\/td>V067<\/a><\/td> matrices trigonalisables<\/em>
\n<\/td>\n<\/tr>\n
<\/td><\/td>compl\u00e9ments<\/em><\/td>\n<\/tr>\n
<\/td><\/td>calcul des puissances par r\u00e9duction <\/em><\/td>\n<\/tr>\n
diagonalisation de matrices<\/em><\/td>exos<\/a><\/td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n<\/div>\n\n\n\n

Espaces pr\u00e9hilbertiens-isom\u00e9tries 2A<\/h2>\n\n\n
\n\n\n\n\n\t\n\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t\n\t
poly epr<\/a><\/th><\/td><\/td>\n<\/tr>\n<\/thead>\n
<\/td>W002<\/a><\/td>d\u00e9finition du produit scalaire<\/em><\/td>\n<\/tr>\n
<\/td>W003<\/a><\/td>produit scalaire usuel sur R^n<\/em><\/td>\n<\/tr>\n
<\/td>W004<\/a><\/td>produit scalaire sur M_n(R)<\/em><\/td>\n<\/tr>\n
<\/td>W005<\/a><\/td>in\u00e9galit\u00e9 de Cauchy-Schwarz<\/em><\/td>\n<\/tr>\n
<\/td>V105<\/a><\/td>proc\u00e9d\u00e9 d'orthonormalisation de Schmidt<\/em><\/td>\n<\/tr>\n
<\/td>W007<\/a><\/td>expression des coordonn\u00e9es dans une bon<\/em><\/td>\n<\/tr>\n
<\/td>W006<\/a><\/td>d\u00e9monstration des th\u00e9o 13 et 14<\/em><\/td>\n<\/tr>\n
poly isom\u00e9tries<\/a><\/td><\/td><\/td>\n<\/tr>\n
<\/td>V111<\/a><\/td>groupe orthogonal d'ordre 3<\/em><\/td>\n<\/tr>\n
<\/td><\/td><\/td>\n<\/tr>\n
<\/td><\/td><\/td>\n<\/tr>\n
<\/td><\/td><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Espaces vectoriels 1A Applications lin\u00e9aires 1A Matrices 1A Compl\u00e9ments d’alg\u00e8bre lin\u00e9aire 2A R\u00e9duction 2A Espaces pr\u00e9hilbertiens-isom\u00e9tries 2A<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-247","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/matimatheque.fr\/index.php?rest_route=\/wp\/v2\/pages\/247","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/matimatheque.fr\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/matimatheque.fr\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/matimatheque.fr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/matimatheque.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=247"}],"version-history":[{"count":12,"href":"https:\/\/matimatheque.fr\/index.php?rest_route=\/wp\/v2\/pages\/247\/revisions"}],"predecessor-version":[{"id":1697,"href":"https:\/\/matimatheque.fr\/index.php?rest_route=\/wp\/v2\/pages\/247\/revisions\/1697"}],"wp:attachment":[{"href":"https:\/\/matimatheque.fr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=247"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}