{"id":70,"date":"2016-07-06T16:09:33","date_gmt":"2016-07-06T14:09:33","guid":{"rendered":"http:\/\/localhost\/wordpress\/?page_id=70"},"modified":"2020-04-11T16:29:40","modified_gmt":"2020-04-11T14:29:40","slug":"linar-algebra","status":"publish","type":"post","link":"https:\/\/www.wolter.tech\/?p=70","title":{"rendered":"Linear Algebra"},"content":{"rendered":"<p>One of the most interesting things I have encountered in linear algebra are pseudospectra and their relation to toeplitz symbol functions, as well as their associated circulant matrix eigenvalues.<br \/>\nBelow I have included plots which illustrate this beautiful relation (click to enlarge in new tab):<\/p>\n<p><center><a href=\"https:\/\/www.wolter.tech\/wordpress\/wp-content\/uploads\/2016\/07\/pesudoMerge.png\" target=\"blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-81\" src=\"https:\/\/www.wolter.tech\/wordpress\/wp-content\/uploads\/2016\/07\/pesudoMerge-300x225.png\" alt=\"pesudoMerge\" width=\"300\" height=\"225\"><\/a><\/center><\/p>\n<p>Shown on the left are the Symbol functions (yellow), Toeplitz eigenvalues (blue) and circulant matrix<br \/>\neigenvalues (green). On the right epsilon-pseudospectra of the same matrices are shown.<\/p>\n<p>Interested? More on:<br \/>\n<a href=\"https:\/\/www.wolter.tech\/wordpress\/wp-content\/uploads\/2016\/07\/pseudospectra.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Pseudospectra<\/a><br \/>\n<a href=\"https:\/\/www.wolter.tech\/wordpress\/wp-content\/uploads\/2016\/07\/regularization.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Regularization<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>One of the most interesting things I have encountered in linear algebra are pseudospectra and their relation to toeplitz symbol functions, as well as their associated circulant matrix eigenvalues. Below I have included plots which illustrate this beautiful relation (click to enlarge in new tab): Shown on the left are the Symbol functions (yellow), Toeplitz &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/www.wolter.tech\/?p=70\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Linear Algebra&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24,6],"tags":[17],"class_list":["post-70","post","type-post","status-publish","format-standard","hentry","category-all","category-master-projects","tag-linear-algebra","entry"],"_links":{"self":[{"href":"https:\/\/www.wolter.tech\/index.php?rest_route=\/wp\/v2\/posts\/70","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.wolter.tech\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.wolter.tech\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.wolter.tech\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.wolter.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=70"}],"version-history":[{"count":13,"href":"https:\/\/www.wolter.tech\/index.php?rest_route=\/wp\/v2\/posts\/70\/revisions"}],"predecessor-version":[{"id":370,"href":"https:\/\/www.wolter.tech\/index.php?rest_route=\/wp\/v2\/posts\/70\/revisions\/370"}],"wp:attachment":[{"href":"https:\/\/www.wolter.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=70"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.wolter.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=70"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.wolter.tech\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=70"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}