{"id":385,"date":"2017-09-14T12:04:41","date_gmt":"2017-09-14T15:04:41","guid":{"rendered":"http:\/\/www.professores.uff.br\/diomarcesarlobao\/?page_id=385"},"modified":"2017-09-14T12:04:41","modified_gmt":"2017-09-14T15:04:41","slug":"fourbase-m","status":"publish","type":"page","link":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/fourbase-m\/","title":{"rendered":"fourbase.m"},"content":{"rendered":"<pre>function [ROW, N, COL, LN] = fourbase(A)\r\n\r\n% fourbase  Bases for all 4 fundamental subspaces. \r\n% \r\n% [ROW, N, COL, LN] = fourbase(A) returns matrices whose columns\r\n% are bases for the row space, nullspace, column space and\r\n% left nullspace of a matrix A.\r\n%\r\n% The bases for all 4 subspaces come from E*A = R.\r\n% The matrix ROW comes from the r pivot rows of R.\r\n% The matrix N comes from the n-r special solutions. \r\n% The matrix COL contains the r pivot columns of A.\r\n% The matrix LN contains the last m-r rows of E.\r\n% Those m-r rows multiply A to give the m-r zero rows in R.\r\n% Notice that A = COL * ROW' .\r\n%\r\n% See also rowbasis, nulbasis, colbasis, leftnull.\r\n\r\n[m, n] = size(A);\r\nr = rank(A);\r\nE = elim(A);\r\n[R, pivcol] = rref(A);\r\nROW = R(1:r, :)'; \r\nN = nulbasis(R);\r\nCOL = A(:, pivcol);\r\nLN = E((r+1):m, :)';\r\n\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>function [ROW, N, COL, LN] = fourbase(A) % fourbase Bases for all 4 fundamental subspaces. % % [ROW, N, COL, LN] = fourbase(A) returns matrices whose columns % are bases for the row space, nullspace, column space and % left nullspace of a matrix A. % % The bases for all 4 subspaces come from [&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-385","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/pages\/385","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=385"}],"version-history":[{"count":1,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/pages\/385\/revisions"}],"predecessor-version":[{"id":386,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/pages\/385\/revisions\/386"}],"wp:attachment":[{"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/media?parent=385"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/categories?post=385"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.professores.uff.br\/diomarcesarlobao\/wp-json\/wp\/v2\/tags?post=385"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}