{"id":398,"date":"2017-09-14T12:08:39","date_gmt":"2017-09-14T15:08:39","guid":{"rendered":"http:\/\/www.professores.uff.br\/diomarcesarlobao\/?page_id=398"},"modified":"2017-09-14T12:08:39","modified_gmt":"2017-09-14T15:08:39","slug":"normal-m","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/normal-m\/","title":{"rendered":"normal.m"},"content":{"rendered":"<pre>function [U, LAMBDA] = normal(A)\r\n\r\n% normal  Eigenvalues and eigenvectors of a normal matrix A.\r\n%\r\n% U = normal(A) returns a set of orthonormal eigenvectors for A.\r\n%\r\n% [U, LAMBDA] = normal(A) also returns the corresponding eigenvalues \r\n% on the diagonal of LAMBDA. The eigenvalues on the diagonal of \r\n% LAMBDA are sorted by magnitude.\r\n%\r\n% Normal matrices (A'*A = A*A') may have complex eigenvalues and \r\n% eigenvectors. If A itself is complex, A' is its conjugate transpose.\r\n%\r\n% See also eig, eigval, eigvec, symmeig.\r\n\r\n[m, n] = size(A);\r\nE = A'*A - A*A';\r\nif norm(E) &lt;= sqrt(eps)\r\n%\r\n% The eigenvectors in S are linearly independent but not orthogonal.\r\n% Eigenvectors for different eigenvalues *are* orthogonal.\r\n% Gram-Schmidt (qr(S)) gives orthonormal eigenvectors in U.\r\n%\r\n  [S, LAMBDA] = eigvec(A);\r\n  [U, R] = qr(S);\r\nelse\r\n  U = []; LAMBDA = [];\r\n  error('The matrix is not normal.');\r\nend<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>function [U, LAMBDA] = normal(A) % normal Eigenvalues and eigenvectors of a normal matrix A. % % U = normal(A) returns a set of orthonormal eigenvectors for A. % % [U, LAMBDA] = normal(A) also returns the corresponding eigenvalues % on the diagonal of LAMBDA. The eigenvalues on the diagonal of % LAMBDA are sorted [&hellip;]<\/p>\n","protected":false},"author":22,"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-398","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/pages\/398","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/comments?post=398"}],"version-history":[{"count":1,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/pages\/398\/revisions"}],"predecessor-version":[{"id":399,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/pages\/398\/revisions\/399"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/media?parent=398"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/categories?post=398"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/tags?post=398"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}