{"id":41,"date":"2017-09-04T13:09:30","date_gmt":"2017-09-04T16:09:30","guid":{"rendered":"http:\/\/www.professores.uff.br\/jcolombo\/?page_id=41"},"modified":"2018-03-13T15:10:42","modified_gmt":"2018-03-13T18:10:42","slug":"algebra-linear-gan00140","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/jcolombo\/algebra-linear-gan00140\/","title":{"rendered":"\u00c1lgebra Linear-GAN00140-Turma B1-2\/2017"},"content":{"rendered":"<dl>\n<dt>\n<hr align=\"center\" size=\"2\" width=\"100%\" \/>\n<\/dt>\n<dt><big><strong>Carga hor\u00e1ria<\/strong>:<\/big>\u00a0 68 hs, turma B1<\/dt>\n<dt><big><strong>Monitoria<\/strong>:<\/big>\u00a0Existem \u00a03 monitores que atendem \u00c1lgebra Linear Aplicada &#8211; Nicole, Tatiana, Douglas \u00a0que atendem na sala 506 do bloco H, \u00a0nos hor\u00e1rios 2\u00aa 14-16hs, 3\u00aa 9-11hs, 4\u00aa 9 -16hs e 5\u00aa 9 -11hs e 6\u00aa 14-16hs.<\/dt>\n<dt><big><strong>Hor\u00e1rio<\/strong>:<\/big> 2\u00aa e 4\u00aa-feiras na sala H-501(UFASA) das 9-11hs.<\/dt>\n<dt><strong>Hor\u00e1rio de atendimento<\/strong>: \u00a0Nas 4\u00aa-feiras das 14-16hs.<\/dt>\n<\/dl>\n<hr \/>\n<p><strong>Listas de Exerc\u00edcios para a P1<br \/>\n<\/strong>1\u00aa Lista &#8211; Exerc\u00edcios 1-24 do cap\u00edtulo 2 do livro do Boldrini [1];<br \/>\n2\u00aa Lista &#8211; Exerc\u00edcios 1-27 do cap\u00edtulo 3 do livro do Boldrini [1];<br \/>\n3\u00aa Lista &#8211; Exerc\u00edcios 1-35 do cap\u00edtulo 4 do livro do Boldrini [1] e os exerc\u00edcios das p\u00e1ginas 160-161 do material refer\u00eancia\u00a0 [0];<br \/>\n4\u00aa Lista &#8211; Exerc\u00edcios 1-29 do cap\u00edtulo 5 do livro do Boldrini [1];<br \/>\n5\u00aa Lista &#8211; Exerc\u00edcios 1-26 do cap\u00edtulo 6 do livro do Boldrini [1].<br \/>\n<strong><br \/>\n<strong>Listas de Exerc\u00edcios para a P2.<\/strong><\/strong><\/p>\n<p>6\u00aa Lista &#8211; Exerc\u00edcios 1-18 do cap\u00edtulo 9, p\u00e1ginas 218-220 do material refer\u00eancia\u00a0 [0];<br \/>\n7\u00aa Lista &#8211; Exerc\u00edcios 1-19 do cap\u00edtulo 8, p\u00e1ginas 247-251 do material refer\u00eancia\u00a0 [1];<br \/>\n8\u00aa Lista &#8211; Exerc\u00edcios 1-14 do cap\u00edtulo 9, p\u00e1ginas 264-267 do material refer\u00eancia\u00a0 [1];<br \/>\n9\u00aa Lista &#8211; Exerc\u00edcios 1-13 do cap\u00edtulo 10, p\u00e1ginas 281-283 do material refer\u00eancia\u00a0 [1];<br \/>\n10\u00aa Lista &#8211; Exerc\u00edcios 1-11 do cap\u00edtulo 11, p\u00e1ginas 305-306 do material refer\u00eancia\u00a0 [1];<\/p>\n<hr \/>\n<dl>\n<dt><strong>Informa\u00e7\u00f5es:<\/strong><b><\/b><\/dt>\n<dt><span class=\"Apple-style-span\">Aqui 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\u00a0ajudar, \u00e9 s\u00f3 me procurar.\u00a0<\/span><\/dt>\n<\/dl>\n<div>\n<ul>\n<li>Mudan\u00e7a de\u00a0coordenadas do sistema CIE-RBG para o sistema CIE-XYZ. (<a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/2-2017-sistemas_de_coordenadas_de_cores.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">pdf<\/a>)<\/li>\n<li><span class=\"Apple-style-span\">Uma aplica\u00e7\u00e3o de \u00e1lgebra linear a\u00a0<a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/2-2017-Tomografia.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">tomografia<\/a>. Este trabalho foi \u00a0apresentado pela Danielle Nascimento monitora de \u00e1lgebra linear no XIV Semana de Monitoria.<\/span><\/li>\n<li><span class=\"Apple-style-span\">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\/2-2017-curto_circuitos.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">pdf<\/a>)<\/span><\/li>\n<\/ul>\n<hr \/>\n<p><a href=\"http:\/\/www.professores.uff.br\/jcolombo\/orientacoes-para-o-estudo-22017\/\">Orienta\u00e7\u00f5es Gerais aos alunos<\/a><\/p>\n<hr \/>\n<p><strong>Data das provas:<\/strong><\/p>\n<p><a href=\"https:\/\/www.professores.uff.br\/jcolombo\/?ddownload=688\" title=\"P1\" rel=\"nofollow\" class=\"ddownload-link id-688 ext-pdf\">P1<\/a> &#8211;\u00a0 09\/10\/2017 &#8211;\u00a0 <a href=\"https:\/\/www.professores.uff.br\/jcolombo\/?ddownload=687\" title=\"Gabarito da P1\" rel=\"nofollow\" class=\"ddownload-link id-687 ext-pdf\">Gabarito da P1<\/a><\/p>\n<p><a href=\"https:\/\/www.professores.uff.br\/jcolombo\/?ddownload=690\" title=\"P2\" rel=\"nofollow\" class=\"ddownload-link id-690 ext-pdf\">P2<\/a> &#8211; \u00a006\/12\/2017 \u00a0&#8211; <a href=\"https:\/\/www.professores.uff.br\/jcolombo\/?ddownload=689\" title=\"Gabarito da P2\" rel=\"nofollow\" class=\"ddownload-link id-689 ext-pdf\">Gabarito da P2<\/a><\/p>\n<\/div>\n<div><a href=\"https:\/\/www.professores.uff.br\/jcolombo\/?ddownload=691\" title=\"VR\" rel=\"nofollow\" class=\"ddownload-link id-691 ext-pdf\">VR<\/a> &#8211; 13\/12\/2017 &#8211;\u00a0 <a href=\"https:\/\/www.professores.uff.br\/jcolombo\/?ddownload=692\" title=\"Gabarito da VR\" rel=\"nofollow\" class=\"ddownload-link id-692 ext-pdf\">Gabarito da VR<\/a><\/div>\n<div><\/div>\n<div><a href=\"https:\/\/www.professores.uff.br\/jcolombo\/?ddownload=693\" title=\"VS\" rel=\"nofollow\" class=\"ddownload-link id-693 ext-pdf\">VS<\/a> &#8211; 20\/12\/2017 \u00a0&#8211; a vista das provas ser\u00e1 dia 21\/12 das \u00a09-10horas em meu gabinete.<\/div>\n<div>\n<dl>\n<dt><b>Cronograma da disciplina<\/b><\/dt>\n<\/dl>\n<p>Aula \u00a0 \u00a0 Data\u00a0\u00a0\u00a0 Assunto<br \/>\n01\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 21\/08 \u00a0\u00a0 Apresenta\u00e7\u00e3o \u00a0da \u00a0disciplina, ementa, bibliografia e avalia\u00e7\u00e3o. Matrizes e Sistemas Lineares<br \/>\n02\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 23\/08 \u00a0\u00a0 Resolu\u00e7\u00e3o de sistemas lineares e matrizes escalonadas, escalonadas reduzidas, posto e nulidade.<br \/>\n03\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 28\/08 \u00a0\u00a0 Determinantes: f\u00f3rmula e t\u00e9cnica de calculo; vetor e espa\u00e7os vetoriais.<br \/>\n04\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 30\/08 \u00a0\u00a0 Subespa\u00e7o vetorial, Combina\u00e7\u00e3o linear, LI.<br \/>\n05 \u00a0\u00a0\u00a0 \u00a0\u00a0\u00a004\/09 \u00a0\u00a0\u00a0Base, dimens\u00e3o, coordenadas.<br \/>\n06\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 06\/09 \u00a0\u00a0 Outras defini\u00e7\u00f5es de determinante, matriz de permuta\u00e7\u00e3o, matrizes elementares, inversa de uma matriz, algoritmo para calcular a inversa de uma matriz.<br \/>\n07\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 11\/09 \u00a0\u00a0\u00a0Mudan\u00e7a de coordenadas. Determinante: det(AB)= det(A) det (B); \u00a0regra de Cramer, adjunta cl\u00e1ssica, \u00e1rea e volume atrav\u00e9s do determinante.<br \/>\n08\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 13\/09 \u00a0\u00a0\u00a0Transforma\u00e7\u00f5es lineares: defini\u00e7\u00e3o<br \/>\n09\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 18\/09 \u00a0\u00a0 Transforma\u00e7\u00f5es lineares: exemplos, n\u00facleo, imagem.<br \/>\n10\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 20\/09 \u00a0\u00a0\u00a0Transforma\u00e7\u00f5es lineares: Teorema do n\u00facleo e da imagem, matriz de uma transforma\u00e7\u00e3o linear<br \/>\n11 \u00a0\u00a0 \u00a0\u00a0\u00a0 25\/09\u00a0 \u00a0 Autovalores e autovetores.<br \/>\n12 \u00a0\u00a0 \u00a0\u00a0\u00a0 27\/09 \u00a0 \u00a0Polin\u00f4mio caracter\u00edstico, dimens\u00e3o alg\u00e9brica e dimens\u00e3o geom\u00e9trica.<br \/>\n13 \u00a0\u00a0 \u00a0\u00a0\u00a0 02\/10 \u00a0 \u00a0Exerc\u00edcios<br \/>\n14 \u00a0\u00a0 \u00a0\u00a0\u00a0 04\/10 \u00a0 \u00a0Exerc\u00edcios<br \/>\n15 \u00a0\u00a0 \u00a0\u00a0\u00a0 09\/10 \u00a0 \u00a0P1<br \/>\n16 \u00a0\u00a0 \u00a0\u00a0\u00a0 11\/10 \u00a0\u00a0 Corre\u00e7\u00e3o da P1, polin\u00f4mio m\u00ednimo, forma can\u00f4nica de Jordan.<br \/>\n17 \u00a0\u00a0 \u00a0\u00a0\u00a0 16\/10 \u00a0 \u00a0Uso do computador &#8211; Forma Can\u00f4nica de Jordan, Produto interno.<br \/>\n18 \u00a0\u00a0 \u00a0\u00a0\u00a0 18\/10 \u00a0 \u00a0Produto interno.<br \/>\n19 \u00a0\u00a0 \u00a0\u00a0\u00a0 23\/10 \u00a0 \u00a0Semana Acad\u00eamica<br \/>\n20 \u00a0\u00a0 \u00a0\u00a0 25\/10 \u00a0\u00a0 Semana Acad\u00eamica<br \/>\n21 \u00a0\u00a0 \u00a0\u00a0\u00a0 30\/10 \u00a0 \u00a0Desigualdade de Cauchy-Schawrz e processo de ortonormaliza\u00e7\u00e3o de Gram-Scmidt.<br \/>\n22 \u00a0\u00a0 \u00a0\u00a0\u00a0 01\/11 \u00a0 \u00a0Operadores Ortogonais e Adjunta de um operador.<br \/>\n23 \u00a0\u00a0 \u00a0\u00a0\u00a0 06\/11 \u00a0 \u00a0Operadores autoadjuntos e o teorema espectral. <a href=\"http:\/\/www.meusiteantigo.uff.br\/jcolombo\/al_GAN00140_20172\/Adjunta_dual.pdf\">Adjunta<\/a><br \/>\n24\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 08\/11 \u00a0 \u00a0Aula de exerc\u00edcios<br \/>\n25\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 13\/11 \u00a0 \u00a0Formas bilineares, quadr\u00e1ticas e matrizes &#8211; teste.<br \/>\n15\/11\u00a0\u00a0\u00a0 Feriado<br \/>\n20\/11\u00a0\u00a0\u00a0 Feriado<br \/>\n22\/11\u00a0\u00a0\u00a0 Feriado<br \/>\n26 \u00a0\u00a0 \u00a0\u00a0\u00a0 27\/11 \u00a0 \u00a0Classifica\u00e7\u00e3o de c\u00f4nicas e formas quadr\u00e1ticas em 3 vari\u00e1veis.<br \/>\n27 \u00a0\u00a0 \u00a0\u00a0\u00a0 29\/11 \u00a0 \u00a0Proje\u00e7\u00e3o ortogonal &#8211; matrizes. Exerc\u00edcios<br \/>\n30 \u00a0\u00a0 \u00a0\u00a0\u00a0 04\/12 \u00a0 \u00a0Aula de Exerc\u00edcios<br \/>\n31 \u00a0\u00a0 \u00a0\u00a0\u00a0 06\/12 \u00a0 \u00a0P2<br \/>\n32 \u00a0\u00a0 \u00a0\u00a0\u00a0 11\/12 \u00a0 \u00a0Vista da P2 e exerc\u00edcios.<br \/>\n33 \u00a0\u00a0 \u00a0\u00a0\u00a0 13\/12 \u00a0 \u00a0VR &#8211; Toda a mat\u00e9ria<br \/>\n32 \u00a0\u00a0 \u00a0\u00a0\u00a0 18\/12 \u00a0 \u00a0Vista da VR<br \/>\n33 \u00a0\u00a0 \u00a0\u00a0\u00a0 20\/12 \u00a0 \u00a0VS &#8211; Toda a mat\u00e9ria<\/p>\n<hr \/>\n<p><strong>Bibliografia:<\/strong><\/p>\n<\/div>\n<p>0) <a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/2-2017-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 Matem\u00e1tica 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. (<a href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2017\/09\/2-2017-gan00140.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Ementa oficial<\/a>).<\/p>\n<hr \/>\n<p>\u00daltima revis\u00e3o em Dezembro, 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:\u00a0 68 hs, turma B1 Monitoria:\u00a0Existem \u00a03 monitores que atendem \u00c1lgebra Linear Aplicada &#8211; Nicole, Tatiana, Douglas \u00a0que atendem na sala 506 do bloco H, \u00a0nos hor\u00e1rios 2\u00aa 14-16hs, 3\u00aa 9-11hs, 4\u00aa 9 -16hs e 5\u00aa 9 -11hs e 6\u00aa 14-16hs. Hor\u00e1rio: 2\u00aa e 4\u00aa-feiras na sala H-501(UFASA) das 9-11hs. Hor\u00e1rio de atendimento: \u00a0Nas [&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-41","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/pages\/41","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=41"}],"version-history":[{"count":22,"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/pages\/41\/revisions"}],"predecessor-version":[{"id":663,"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/pages\/41\/revisions\/663"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/media?parent=41"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/categories?post=41"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/tags?post=41"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}