{"id":1290,"date":"2019-08-16T16:39:00","date_gmt":"2019-08-16T19:39:00","guid":{"rendered":"http:\/\/www.professores.uff.br\/jcolombo\/?page_id=1290"},"modified":"2019-12-10T17:29:36","modified_gmt":"2019-12-10T20:29:36","slug":"algebra-linear-ii-2019_2","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/jcolombo\/algebra-linear-ii-2019_2\/","title":{"rendered":"\u00c1lgebra Linear II &#8211; 2019_2"},"content":{"rendered":"\n<p><strong>Carga hor\u00e1ria:<\/strong> 68 hs, turma B1<\/p>\n\n\n\n<p><strong>Informa\u00e7\u00f5es:<\/strong><br>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 ajudar, \u00e9 s\u00f3 me procurar.<\/p>\n\n\n\n<ul class=\"wp-block-list\"><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=\"noreferrer noopener\">pdf<\/a>)<\/li><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=\"noreferrer noopener\">tomografia<\/a>. Este trabalho foi apresentado pela Danielle Nascimento monitora de \u00e1lgebra linear no XIV Semana de Monitoria.<\/li><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=\"noreferrer noopener\">pdf<\/a>)<\/li><\/ul>\n\n\n\n<hr class=\"wp-block-separator\" \/>\n\n\n\n<hr class=\"wp-block-separator\" \/>\n\n\n\n<p><strong>Lista de Exerc\u00edcios para a P1<\/strong><br>\nLista 1 &#8211; Exerc\u00edcios p\u00e1g   91-95 referentes ao cap\u00edtulo 05 de [1].   <br>\nLista 2 &#8211; Exerc\u00edcios p\u00e1g. 147-151 referentes ao cap\u00edtulo 07 de [1].  <br>\nLista 3 &#8211; Exerc\u00edcios p\u00e1g. 353-356 referentes ao cap\u00edtulo 10 de [2].  <br>\nLista 4 &#8211; Exerc\u00edcios p\u00e1g. 365-366 referentes ao cap\u00edtulo 11 de [2].  <br>\n<\/p>\n\n\n\n<hr class=\"wp-block-separator\" \/>\n\n\n\n<p><strong>Hor\u00e1rio:<\/strong> 3\u00aa e 5\u00aa-feiras na sala IM-304G das 11 \u00e0s 13hs.<br><strong>Meu hor\u00e1rio de atendimento:<\/strong> 4\u00aa-feiras, das 14-18hs em meu gabinete.<\/p>\n\n\n\n<hr class=\"wp-block-separator\" \/>\n\n\n\n<p><strong>Provas<\/strong><br><a rel=\"noreferrer noopener\" href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2019\/10\/P1AlgLin_II.pdf\" target=\"_blank\">P1<\/a> &#8211; 01\/10\/2019<br><a rel=\"noreferrer noopener\" href=\"http:\/\/www.professores.uff.br\/jcolombo\/wp-content\/uploads\/sites\/124\/2019\/12\/P2_AlgLin_II.pdf\" target=\"_blank\">P2<\/a> &#8211; 05\/12\/2019<br>VR &#8211; 12\/12\/2019 (alteramos para  17\/12\/2019 &#8211; toda a mat\u00e9ria.)<br>VS &#8211; 17\/12\/2019 (alteramos para 19\/12\/2019)<\/p>\n\n\n\n<hr class=\"wp-block-separator\" \/>\n\n\n\n<p><strong>Cronograma<\/strong><\/p>\n\n\n\n<p><strong>Aula \u00a0 \u00a0 Data\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Assunto<\/strong><br>01\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0 13\/08\u00a0\u00a0\u00a0\u00a0 Apresenta\u00e7\u00e3o \u00a0da \u00a0disciplina, ementa, bibliografia e Avalia\u00e7\u00e3o.<br>02\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 15\/08\u00a0\u00a0\u00a0 Operadores diagonaliz\u00e1veis, soma direta e proje\u00e7\u00f5es.<br>03\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 20\/08\u00a0\u00a0\u00a0 Polin\u00f4mio m\u00ednimo, complexifica\u00e7\u00e3o de um espa\u00e7o vetorial.<br>04 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 22\/08   &nbsp;&nbsp;&nbsp;  Subespa\u00e7o T-invariante, Interpola\u00e7\u00e3o de Lagrange e operadores proje\u00e7\u00e3o.<br>\n05 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 27\/08   &nbsp;&nbsp;&nbsp;  Exerc\u00edcios e revis\u00e3o sobre MDC.<br>\n06 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 29\/08   &nbsp;&nbsp;&nbsp;  Demonstra\u00e7\u00e3o do Teorema da Decomposi\u00e7\u00e3o Prim\u00e1ria.<br>\n07 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 03\/09   &nbsp;&nbsp;&nbsp;  Decomposi\u00e7\u00e3o de Jordan.<br>\n08 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 05\/09   &nbsp;&nbsp;&nbsp;  Decomposi\u00e7\u00e3o de Jordan Real.<br>\n09 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 10\/09   &nbsp;&nbsp;&nbsp;  Aula de exerc\u00edcios adjunto e transposta.<br>\n10 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 12\/09   &nbsp;&nbsp;&nbsp;  Aula de exerc\u00edcios, operadores nilpotentes.  <br>\n11 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 17\/09   &nbsp;&nbsp;&nbsp;  Aula de exerc\u00edcios: operadores que s\u00e3o diagonaliz\u00e1veis simultaneamente, detalhes sobre a forma can\u00f4nica de Jordan de um operador nilpotente.<br>\n12 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 19\/09   &nbsp;&nbsp;&nbsp;  Aula de exerc\u00edcios: Soma direta. <br>\n13 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 24\/09   &nbsp;&nbsp;&nbsp;  Aula de exerc\u00edcios e funcionais.<br>\n14 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 26\/09   &nbsp;&nbsp;&nbsp;  Aula de exerc\u00edcios.<br>\n15 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 01\/10   &nbsp;&nbsp;&nbsp;  P1.<br>\nXX &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 03\/10   &nbsp;&nbsp;&nbsp;  N\u00e3o teremos aula. <br>\n16 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 08\/10   &nbsp;&nbsp;&nbsp;  Corre\u00e7\u00e3o da P1 e Produto Interno. <br>\n17 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 10\/10   &nbsp;&nbsp;&nbsp;  Produto Interno: Processo de ortonormaliza\u00e7\u00e3o de Gram-Schmidt. <br>\nXX &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 15\/10   &nbsp;&nbsp;&nbsp;  N\u00e3o teve aula. <br>\n18 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 17\/10   &nbsp;&nbsp;&nbsp;  Adjunta: Equa\u00e7\u00e3o normal, operadores especiais. O Teorema Espectral. <br>\nXX &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 22\/10   &nbsp;&nbsp;&nbsp;  Semana Acad\u00eamica. <br>\nXX &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 24\/10   &nbsp;&nbsp;&nbsp;  Semana Acad\u00eamica. <br>\n19 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 29\/10   &nbsp;&nbsp;&nbsp;   Exemplo do Teorema espectral e in\u00edcio do estudo de operadores ortogonais. <br>\n20 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 31\/10   &nbsp;&nbsp;&nbsp;  Operadores ortogonais em R^2 e em R^3: Proje\u00e7\u00f5es e Reflex\u00f5es. Enunciei o teorema dos valores singulares. <br>\nXX &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 05\/11   &nbsp;&nbsp;&nbsp;  N\u00e3o teremos aula. <br>\nXX &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 07\/11   &nbsp;&nbsp;&nbsp;  N\u00e3o teremos aula. <br>\n21 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 12\/11   &nbsp;&nbsp;&nbsp;  Teorema dos Valores Singulares, decomposi\u00e7\u00e3o polar, fatora\u00e7\u00e3o QR &#8211; matrizes de Householder. <br>\n22 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 14\/11   &nbsp;&nbsp;&nbsp;   \nFormas bilineares sim\u00e9tricas e anti-sim\u00e9tricas. Formas quadr\u00e1ticas (sinal). Reconhecimento de c\u00f4nicas e qu\u00e1dricas. <br>\n21 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 19\/11   &nbsp;&nbsp;&nbsp;   Aula de exerc\u00edcios. <br>\nXX &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 21\/11   &nbsp;&nbsp;&nbsp;  Feriado. <br>\n22 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 25\/11   &nbsp;&nbsp;&nbsp;  Aula de exerc\u00edcios. 14h <br>\nXX &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 26\/11   &nbsp;&nbsp;&nbsp;  N\u00e3o teremos aula. <br>\n23 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 28\/11   &nbsp;&nbsp;&nbsp;  Aula de exerc\u00edcios. <br>\n24 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 03\/12   &nbsp;&nbsp;&nbsp;  Aula de exerc\u00edcios. <br>\n25 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 05\/12   &nbsp;&nbsp;&nbsp;  P2. <br>\n26 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 10\/12   &nbsp;&nbsp;&nbsp;  Vista da P2 e aula de exerc\u00edcios. <br>\n27 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 12\/12   &nbsp;&nbsp;&nbsp;  Aula de exerc\u00edcios. <br>\n28 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 17\/12   &nbsp;&nbsp;&nbsp;  VR. <br>\n29 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 19\/12   &nbsp;&nbsp;&nbsp;  VS. <br>\n\n\n\n<p><br><br><\/p>\n\n\n\n<hr class=\"wp-block-separator\" \/>\n\n\n\n<p><strong>Bibliografia:<\/strong><br>[1] \u00c1lgebra Linear: um segundo curso: Hamilton S. Bueno <br>[2]  \u00c1lgebra Linear, S. Lipschutz; M.L. Lipson, Cole\u00e7\u00e3o Schaum, Bookman, 4\u00aa edi\u00e7\u00e3o, 2011.  <br>[3]  \u00c1lgebra Linear, Hoffman, K., Kunze, R. Prentice-Hall, INC, Englewood Cliff, New Jersey, 1971. <br>[4] Contemporary Linear Algebra, Anton,H, Busby, Robert C., John Wiley &amp; Sons, Inc.<br> [6] \u00c1lgebra Linear, E.L. Lima, Cole\u00e7\u00e3o Matematica Universit\u00e1ria, 2\u00aa edi\u00e7\u00e3o, 1996.<br>[7] <\/p>\n\n\n\n<hr class=\"wp-block-separator\" \/>\n\n\n\n<p><strong>Ementa:<br><\/strong><\/p>\n\n\n\n<p>Subespa\u00e7os invariantes, Teorema da Decomposi\u00e7\u00e3o Prim\u00e1ria, Forma can\u00f4nica de Jordan (real e complexa). <\/p>\n<p>Funcionais lineares, espa\u00e7o dual. <\/p>\n<p>Espa\u00e7os com produto interno, ortogonalidade, bases ortonormais, processo de Gram-Schmidt, operadores em espa\u00e7os com produto interno,  espa\u00e7os normados e operadores ortogonais, classifica\u00e7\u00e3o de isometrias.<\/p>\n<p>Operadores auto-adjuntos, Teorema Espectral (diagonaliza\u00e7\u00e3o de operadores auto-adjuntos), Teorema dos Valores Singulares. <\/p>\n<p>Formas bilineares sim\u00e9tricas e anti-sim\u00e9tricas, Formas quadr\u00e1ticas (sinal), reconhecimento de c\u00f4nicas e qu\u00e1dricas.<\/p>\n<p>T\u00f3picos Opcionais: Forma Can\u00f4nica Racional, Decomposi\u00e7\u00e3o QR, Decomposi\u00e7\u00e3o LU, Decomposi\u00e7\u00e3o em valores singulares (SVD), Produto tensorial e \u00e1lgebra exterior. <\/p>\n\n\n\n<p><\/p>\n\n\n\n<hr class=\"wp-block-separator\" \/>\n\n\n\n<p>\u00daltima revis\u00e3o em Novembro, 2019.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carga hor\u00e1ria: 68 hs, turma B1 Informa\u00e7\u00f5es: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 ajudar, \u00e9 s\u00f3 me procurar. Mudan\u00e7a de coordenadas do sistema CIE-RBG para o sistema CIE-XYZ. (pdf) Uma [&hellip;]<\/p>\n","protected":false},"author":129,"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-1290","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/pages\/1290","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\/129"}],"replies":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/comments?post=1290"}],"version-history":[{"count":35,"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/pages\/1290\/revisions"}],"predecessor-version":[{"id":1439,"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/pages\/1290\/revisions\/1439"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/media?parent=1290"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/categories?post=1290"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/jcolombo\/wp-json\/wp\/v2\/tags?post=1290"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}