{"id":108,"date":"2017-09-05T10:32:52","date_gmt":"2017-09-05T13:32:52","guid":{"rendered":"http:\/\/www.professores.uff.br\/jcolombo\/?page_id=108"},"modified":"2017-09-18T11:23:47","modified_gmt":"2017-09-18T14:23:47","slug":"algebra-llinear-gan00140","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/jcolombo\/algebra-llinear-gan00140\/","title":{"rendered":"\u00c1lgebra Llinear &#8211; GAN00140 &#8211; Turma H1 &#8211; 1\/2017"},"content":{"rendered":"<p><strong>Carga hor\u00e1ria:<\/strong> 60 hs, turma H1<br \/>\n<strong>Monitoria:<\/strong><br \/>\n<strong>Hor\u00e1rio:<\/strong> 3\u00aa e 5\u00aa-feiras na sala H-404 (UFASA) das 16-18hs.<br \/>\n<strong>Hor\u00e1rio de atendimento:<\/strong> 4\u00aa-feiras das 14-18 no meu gabinete. Gabinete 4, no 4\u00aa andar do pr\u00e9dio da Matem\u00e1tica no Valonguinho<\/p>\n<hr \/>\n<p><strong>Listas de Exerc\u00edcios para a P1<\/strong><br \/>\n1\u00aa lista de exerc\u00edcios &#8211; lista de exerc\u00edcios do cap\u00edtulo 2 do livro do Boldrini [refer\u00eancia 1].<br \/>\n2\u00aa lista de exerc\u00edcios &#8211; lista de exerc\u00edcios do cap\u00edtulo 4 do livro do Boldrini [refer\u00eancia 1].<br \/>\n3\u00aa lista de exerc\u00edcios &#8211; lista de exerc\u00edcios do cap\u00edtulo 5 do livro do Boldrini [refer\u00eancia 1].<br \/>\n4\u00aa lista de exerc\u00edcios &#8211; lista de exerc\u00edcios do cap\u00edtulo 7 da apostila Koiller&amp;Colombo [refer\u00eancia 0].<br \/>\n5\u00aa lista de exerc\u00edcios &#8211; lista de exerc\u00edcios do cap\u00edtulo 3 do livro do Boldrini [refer\u00eancia 1].<\/p>\n<p><strong>Listas de Exerc\u00edcios para a P2<\/strong><br \/>\n1\u00aa lista de exerc\u00edcios &#8211; lista de exerc\u00edcios do cap\u00edtulo 6 do livro do Boldrini [refer\u00eancia 1].<br \/>\n2\u00aa lista de exerc\u00edcios &#8211; lista de exerc\u00edcios do cap\u00edtulo 7 do livro do Boldrini [refer\u00eancia 1].<br \/>\n3\u00aa lista de exerc\u00edcios &#8211; exerc\u00edcios do cap\u00edtulo 8 da refer\u00eancia bibliogr\u00e1fica 1.<br \/>\n4\u00aa lista de exerc\u00edcios &#8211; exerc\u00edcios do cap\u00edtulo 9 da refer\u00eancia bibliogr\u00e1fica 1.<br \/>\n5\u00aa lista de exerc\u00edcios &#8211; exerc\u00edcios do cap\u00edtulo 11 da refer\u00eancia bibliogr\u00e1fica 1.<\/p>\n<hr \/>\n<p><strong>Informa\u00e7\u00f5es:<\/strong><br \/>\nAqui est\u00e3o alguns arquivos em pdf que baixei da rede e que tem aplica\u00e7\u00f5es de \u00e1lgebra linear. Caso algu\u00e9m queira ler algum destes arquivos e esteja encontrando dificuldades eu teria muito prazer ajudar, \u00e9 s\u00f3 me procurar.<\/p>\n<ul>\n<li>Mudan\u00e7a de coordenadas do sistema CIE-RBG para o sistema CIE-XYZ. (<a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/1-2017-sistemas_de_coordenadas_de_cores.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">pdf<\/a>)<\/li>\n<li>Uma aplica\u00e7\u00e3o de \u00e1lgebra linear a <a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/1-2017-Tomografia.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">tomografia<\/a>. Este trabalho foi apresentado pela Danielle Nascimento monitora de \u00e1lgebra linear no XIV Semana de Monitoria.<\/li>\n<li>Utiliza\u00e7\u00e3o de \u00e1lgebra linear em Circuitos El\u00e9tricos. (<a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/1-2017-curto_circuitos.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">pdf<\/a>)<\/li>\n<\/ul>\n<hr \/>\n<p><a href=\"http:\/\/www.professores.uff.br\/jcolombo\/orientacoes-para-o-estudo\/\"><strong>Orienta\u00e7\u00f5es Gerais aos alunos<\/strong><\/a><\/p>\n<hr \/>\n<p><strong>Datas das Provas:<\/strong><br \/>\n<a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/1-2017-P1_AL_20171.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">P1<\/a> &#8211; 09\/05\/2017<br \/>\n<a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/1-2017-Prova2AL.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">P2<\/a> &#8211; 04\/07\/2017 (<a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/1-2017-Prova2AL_gabarito.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">gabarito da P2<\/a>)<br \/>\n<a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/1-2017-ProvaVRAL.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">VR<\/a> -11\/07\/2017 (<a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/1-2017-ProvaVRAL_Gabarito.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">gabarito da VR<\/a>) Vista de provas das 14-15hs do dia 13\/07 em meu gabinete.<br \/>\n<a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/1-2017-ProvaVSAL.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">VS<\/a> -13\/07\/2017 (<a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/1-2017-Notas_VS_14_JUL_2017_ALGL_linear.txt\" target=\"_blank\" rel=\"noopener noreferrer\">notas<\/a>) Vista da VS das 14-16hs do dia 17\/07 em meu gabinete.<\/p>\n<hr \/>\n<p><strong>Cronograma da disciplina<\/strong><\/p>\n<p>Aula \u00a0 \u00a0 Data\u00a0\u00a0\u00a0 Assunto<br \/>\n01\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 21\/03\u00a0\u00a0\u00a0\u00a0Apresenta\u00e7\u00e3o \u00a0da \u00a0disciplina, ementa, bibliografia e avalia\u00e7\u00e3o.<br \/>\n02\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 23\/03\u00a0\u00a0\u00a0\u00a0Resolu\u00e7\u00e3o de sistemas lineares e matrizes.<br \/>\n03\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 28\/03\u00a0\u00a0\u00a0\u00a0Matrizes Escalonadas reduzida, posto, nulidade e\u00a0 solu\u00e7\u00e3o de sistemas lineares.<br \/>\n04\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 30\/03\u00a0\u00a0\u00a0\u00a0Matrizes elementares, matrizes invert\u00edveis, matrizes triangulares, fatora\u00e7\u00e3o LU.<br \/>\n05 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a004\/04\u00a0\u00a0\u00a0\u00a0Espa\u00e7os vetoriais &#8211; Axiomas, propriedades elementares.<br \/>\n06\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 06\/04\u00a0\u00a0\u00a0 Conjunto gerado, linearmente dependente e independente, base.<br \/>\n07\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 11\/04\u00a0\u00a0\u00a0 A invari\u00e2n\u00e7a da quantidades de vetores na base,\u00a0dimens\u00e3o, coordenadas.<br \/>\n08\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 13\/04\u00a0\u00a0\u00a0 Matriz de mudan\u00e7a de coordenadas,\u00a0 exerc\u00edcios.<br \/>\n09\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 18\/04\u00a0\u00a0\u00a0\u00a0Operadores lineares: N\u00facleo, Imagem, Rota\u00e7\u00f5es.<br \/>\n10\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 20\/04\u00a0\u00a0\u00a0\u00a0Teorema do N\u00facleo e da Imagem.\u00a0Operadores lineares: Matrizes.<br \/>\n11 \u00a0\u00a0 \u00a0\u00a0\u00a0 25\/04\u00a0\u00a0 \u00a0Exemplos de operadores lineares e matrizes<br \/>\n12 \u00a0\u00a0 \u00a0\u00a0\u00a0 27\/04 \u00a0 \u00a0Aula de exerc\u00edcios<br \/>\n13 \u00a0\u00a0 \u00a0\u00a0\u00a0 02\/05 \u00a0\u00a0 Determinantes: Introdu\u00e7\u00e3o, expans\u00e3o de Laplace, propriedades b\u00e1sicas<br \/>\n14 \u00a0\u00a0 \u00a0\u00a0\u00a0 04\/05 \u00a0 \u00a0Aula de exerc\u00edcios<br \/>\n15 \u00a0\u00a0 \u00a0\u00a0\u00a0 09\/05 \u00a0\u00a0\u00a0<a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/1-2017-P1_AL_20171.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">P1<\/a><br \/>\n16 \u00a0\u00a0 \u00a0\u00a0\u00a0 11\/05 \u00a0\u00a0 Revis\u00e3o da P1 e processo de diagonaliza\u00e7\u00e3o<br \/>\n17 \u00a0\u00a0 \u00a0\u00a0\u00a0 16\/05 \u00a0 \u00a0processo de diagonaliza\u00e7\u00e3o \u00a0&#8211; \u00a0estudo de casos<br \/>\n18 \u00a0\u00a0 \u00a0\u00a0\u00a0 18\/05 \u00a0\u00a0 processo de diagonaliza\u00e7\u00e3o &#8211; teorema de Cayley, polin\u00f4mio m\u00ednimo, dimens\u00e3o alg\u00e9brica e geom\u00e9trica<br \/>\n19 \u00a0\u00a0 \u00a0\u00a0\u00a0 23\/05 \u00a0 \u00a0Forma de Jordan &#8211; e coment\u00e1rios sobre os outros conceitos e resultados<br \/>\n20 \u00a0\u00a0 \u00a0\u00a0\u00a0 25\/05 \u00a0\u00a0 Produto Interno<br \/>\n21 \u00a0\u00a0 \u00a0\u00a0\u00a0 30\/05 \u00a0\u00a0 Produto Interno &#8211; Processo de ortonormaliza\u00e7\u00e3o de Gram-Schimdt<br \/>\n22 \u00a0\u00a0 \u00a0\u00a0\u00a0 01\/06 \u00a0 \u00a0Operadores Autoadjuntos<br \/>\n23 \u00a0\u00a0 \u00a0\u00a0\u00a0 06\/06 \u00a0 \u00a0Aula de\u00a0Exerc\u00edcios (ref [1], p\u00e1g 214 ex 6,7,8.\u00a0 P\u00e1g 247 ex 5, 9,10 e 11. P\u00e1g 264 ex.7)<br \/>\n24 \u00a0\u00a0 \u00a0\u00a0\u00a0 08\/06 \u00a0\u00a0\u00a0Aula de\u00a0Exerc\u00edcios (ref [1], p\u00e1g 214 ex 6,7,8.\u00a0 P\u00e1g 247 ex 5, 9,10 e 11. P\u00e1g 264 ex.7)<br \/>\n25 \u00a0\u00a0 \u00a0\u00a0\u00a0 13\/06 \u00a0\u00a0\u00a0Exerc\u00edcios 9, 10 e 11 da p\u00e1g 265 &#8211;\u00a0Outra prova do teorema espectral + mudan\u00e7a de coordenadas + Classifica\u00e7\u00e3o das C\u00f4nicas<br \/>\n15\/06 \u00a0 \u00a0Feriado Corpus Christi<br \/>\n26 \u00a0\u00a0 \u00a0\u00a0\u00a0 20\/06 \u00a0 \u00a0Aula de exerc\u00edcios\u00a0 &#8211; matrizes de proje\u00e7\u00e3o &#8211; forma normal de um sistema de equa\u00e7\u00f5es lineares.<br \/>\n27 \u00a0\u00a0 \u00a0\u00a0\u00a0 22\/06 \u00a0\u00a0\u00a0C\u00f4nicas no espa\u00e7o, \u00a0matrizes de proje\u00e7\u00e3o ortogonal<br \/>\n28 \u00a0\u00a0 \u00a0\u00a0\u00a0 27\/06 \u00a0\u00a0\u00a0Aula de Exerc\u00edcios<br \/>\n29 \u00a0\u00a0 \u00a0\u00a0\u00a0 29\/06 \u00a0 \u00a0Aula de Exerc\u00edcios<br \/>\n30 \u00a0\u00a0 \u00a0\u00a0\u00a0 04\/07 \u00a0\u00a0\u00a0<a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/1-2017-ProvaVRAL.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">P2<\/a><br \/>\n31 \u00a0\u00a0 \u00a0\u00a0\u00a0 06\/07 \u00a0 \u00a0<a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/1-2017-ProvaVRAL_Gabarito.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Corre\u00e7\u00e3o da P2<\/a>.<br \/>\n32 \u00a0\u00a0 \u00a0\u00a0\u00a0 11\/07 \u00a0\u00a0\u00a0VR<br \/>\n33 \u00a0\u00a0 \u00a0\u00a0\u00a0 13\/07 \u00a0\u00a0\u00a0VS<strong><br \/>\n<\/strong><\/p>\n<hr \/>\n<p><strong>Bibliografia:<\/strong><\/p>\n<p>0) <a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/1-2017-NotasColomboKoiller_EM_PREPARACAO.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">\u00c1lgebra Linear: Texto em prepara\u00e7\u00e3o<\/a>, Jones Colombo e Jos\u00e9 Koiller.<br \/>\n1) \u00c1lgebra Linear, Boldrini, Costa, Ribeiro,Wetzler, Editora Harbra, 3\u00aa edi\u00e7\u00e3o.<br \/>\n2) Contemporary Linear Algebra, Anton,H, Busby, Robert C., John Wiley &amp; Sons, Inc.<br \/>\n3) \u00c1lgebra Linear, Seymour Lipschutz, Cole\u00e7\u00e3o Schaum, MacGraw-Hill, 2\u00aa edi\u00e7\u00e3o, 1972.<br \/>\n3) \u00c1lgebra Linear e Aplica\u00e7\u00f5es, Carlos A. Callioli , Hygino H. Domingues, Roberto C.F. Costa, Editora Atual,6\u00aa edi\u00e7\u00e3o, 1990.<br \/>\n5) \u00c1lgebra Linear, S. Lang, Editora Edgar Blucher Ltda, 1971.<br \/>\n6) \u00c1lgebra Linear, E.L. Lima, Cole\u00e7\u00e3o Matematica Universit\u00e1ria, 2\u00aa edi\u00e7\u00e3o, 1996.<br \/>\n7) \u00c1lgebra Linear, Hoffman, K., Kunze, R. Prentice-Hall, INC, Englewood Cliff, New Jersey, 1971.<\/p>\n<hr \/>\n<p><strong>Ementa:<\/strong> 1. Matrizes: Defini\u00e7\u00e3o, igualdade e opera\u00e7\u00f5es matriciais, 2. Determinantes: Defini\u00e7\u00e3o, propriedades, e m\u00e9todos de c\u00e1lculo, 3. Sistemas lineares, 4. Espa\u00e7os vetoriais: Defini\u00e7\u00e3o e exemplos. Subespa\u00e7os vetoriais. Soma direta, 5. Espa\u00e7os vetoriais: Depend\u00eancia e independ\u00eancia linear, base e dimens\u00e3o, 6. Transforma\u00e7\u00f5es lineares: Defini\u00e7\u00e3o, propriedades, n\u00facleo e imagem, 7. Transforma\u00e7\u00f5es lineares: Representa\u00e7\u00e3o por matrizes. Teorema do posto, 8. Exemplos de transforma\u00e7\u00f5es lineares no plano e no espa\u00e7o, 9. Transforma\u00e7\u00f5es lineares: Mudan\u00e7a de base, 10. Semelhan\u00e7a de matrizes e operadores, 11. Produto interno: Defini\u00e7\u00e3o e exemplos. Vetores e subespa\u00e7os ortogonais, 12. Processo de Ortogonaliza\u00e7\u00e3o de Gram-Schmidt, 13. Autovalores e Autovetores: Defini\u00e7\u00e3o e exemplos. Obten\u00e7\u00e3o dos autovetores. Matrizes diagonaliz\u00e1veis, 14. Diagonaliza\u00e7\u00e3o de matrizes sim\u00e9tricas, 15. Formas quadr\u00e1ticas no plano: Defini\u00e7\u00e3o c\u00f4nicas, identifica\u00e7\u00e3o de c\u00f4nicas. (Ementa oficial).<\/p>\n<hr \/>\n<p>\u00daltima revis\u00e3o em Julho, 2017.<\/p>\n<p style=\"text-align: center;\"><strong><a href=\"http:\/\/www.professores.uff.br\/jcolombo\/disciplinas\/\">Voltar<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carga hor\u00e1ria: 60 hs, turma H1 Monitoria: Hor\u00e1rio: 3\u00aa e 5\u00aa-feiras na sala H-404 (UFASA) das 16-18hs. Hor\u00e1rio de atendimento: 4\u00aa-feiras das 14-18 no meu gabinete. Gabinete 4, no 4\u00aa andar do pr\u00e9dio da Matem\u00e1tica no Valonguinho Listas de Exerc\u00edcios para a P1 1\u00aa lista de exerc\u00edcios &#8211; lista de exerc\u00edcios do cap\u00edtulo 2 do [&hellip;]<\/p>\n","protected":false},"author":70,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"categories":[],"tags":[],"class_list":["post-108","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/pages\/108","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/users\/70"}],"replies":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/comments?post=108"}],"version-history":[{"count":13,"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/pages\/108\/revisions"}],"predecessor-version":[{"id":642,"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/pages\/108\/revisions\/642"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/media?parent=108"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/categories?post=108"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/tags?post=108"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}