{"id":3794,"date":"2008-06-27T15:08:00","date_gmt":"2008-06-27T06:08:00","guid":{"rendered":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/?p=3794"},"modified":"2021-08-12T12:00:53","modified_gmt":"2021-08-12T03:00:53","slug":"univmathcomp-200806","status":"publish","type":"post","link":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/2008\/06\/27\/univmathcomp-200806\/","title":{"rendered":"UnivMathComp\/200806"},"content":{"rendered":"<div id=\"outline-container-orgb5e2960\" class=\"outline-2\">\n<h2 id=\"orgb5e2960\">Linear algebra: Kenneth Hoffman<\/h2>\n<div class=\"outline-text-2\" id=\"text-orgb5e2960\">\n<p> Section 3.4 <\/p>\n<p> Exercise <\/p>\n<ol class=\"org-ol\">\n<li>Let $ V $  be a finite-dimensional vector space over the field $ F $  and let $ S $  and $ T $  be linear operators on $ V $ . We ask: When do there exist ordered bases $ B $  and $ B&#8217;  $  for $ V $  such that $ [S]_B=[T]_{B&#8217;} $  ?<\/li>\n<\/ol>\n<p> (proof) <\/p>\n<p> We want to show that $ [S]_B=[T]_{B&#8217;} $ \u21d4 \u2203invertible linear operator $ U $   such that $ T=USU^{-1} $ . <\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Linear algebra: Kenneth Hoffman Section 3.4 Exercise Let $ V $ be a finite-dimensional vector space over the field $ F $ and let $ S $ and $ T $ be linear operators on $ V $ . We ask: When do there exist ordered bases $ B $ and $ B&#8217; $ for &#8230; <a title=\"UnivMathComp\/200806\" class=\"read-more\" href=\"https:\/\/mathematicians.korea.ac.kr\/ywkim\/2008\/06\/27\/univmathcomp-200806\/\" aria-label=\"UnivMathComp\/200806\uc5d0 \ub300\ud574 \ub354 \uc790\uc138\ud788 \uc54c\uc544\ubcf4\uc138\uc694\">\ub354 \uc77d\uae30<\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-3794","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"distributor_meta":false,"distributor_terms":false,"distributor_media":false,"distributor_original_site_name":"\uae40\uc601\uc6b1","distributor_original_site_url":"https:\/\/mathematicians.korea.ac.kr\/ywkim","push-errors":false,"_links":{"self":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3794","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/comments?post=3794"}],"version-history":[{"count":1,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3794\/revisions"}],"predecessor-version":[{"id":3795,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/posts\/3794\/revisions\/3795"}],"wp:attachment":[{"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/media?parent=3794"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/categories?post=3794"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematicians.korea.ac.kr\/ywkim\/wp-json\/wp\/v2\/tags?post=3794"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}