{"id":3758,"date":"2024-03-08T15:17:36","date_gmt":"2024-03-08T20:17:36","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/boyland\/?page_id=3758"},"modified":"2026-03-19T08:10:23","modified_gmt":"2026-03-19T12:10:23","slug":"igor-klep-2","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/boyland\/igor-klep-2\/","title":{"rendered":"Igor Klep"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">Igor Klep<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">Joint similarity of matrix tuples.<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Abstract: This talk will discuss a classical problem in matrix theory: when are two tuples of matrices similar? We solve the two-sided version of the 2003 conjecture of Hadwin and Larson, itself an updated version of a 1985 conjecture of Curto and Herrero. Consider evaluations of linear pencils L = T_0 + x_1 T_1 + &#8230; + x_m T_m on matrix tuples using Kronecker&#8217;s tensor product by L(X_1,&#8230;,X_m) := I \u2297 T_0 + X_1 \u2297 T_1 + &#8230; + X_m \u2297 T_m. We will show that ranks of linear pencils constitute a collection of separating invariants for simultaneous similarity of matrix tuples. That is, m-tuples A and B of n \u00d7 n matrices are simultaneously similar if and only if the ranks of L(A) and L(B) are equal for all linear matrix pencils L of size mn. Variants of this property exist for symplectic, orthogonal, unitary similarity, and for the left-right action of general linear groups. Finally, if time permits, a polynomial time algorithm for orbit equivalence of matrix tuples under the left-right action of special linear groups will be presented. The talk is based on joint work with Harm Derksen, Visu Makam and Jurij Vol\u010di\u010d.<\/p>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":146,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-3758","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/3758","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/users\/146"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/comments?post=3758"}],"version-history":[{"count":2,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/3758\/revisions"}],"predecessor-version":[{"id":3785,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/3758\/revisions\/3785"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/media?parent=3758"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}