{"id":647,"date":"2025-09-08T20:17:23","date_gmt":"2025-09-08T19:17:23","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/tfg\/?p=647"},"modified":"2026-02-13T08:16:58","modified_gmt":"2026-02-13T07:16:58","slug":"matrius-enteres-un-univers-parallel-inesperat","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/tfg\/matrius-enteres-un-univers-parallel-inesperat\/","title":{"rendered":"Matrius enteres, un univers paral\u00b7lel inesperat"},"content":{"rendered":"<p>La teoria de matrius enteres combina l&#8217;\u00e0lgebra lineal amb la teoria de grups i la teoria de nombres. Com el determinant de la inversa d&#8217;una matriu \u00e9s l&#8217;invers del determinant, per tal de tindre un grup, es consideren matrius amb determinant $\\pm 1$ ($\\textup{GL}(n,\\mathbb{Z}))$) o $1$ ($\\textup{SL}(n,\\mathbb{Z}))$). Algunes q\u00fcestions interessants que hi apareixen s\u00f3n si hi ha un an\u00e0leg a la forma can\u00f2nica de Jordan (si solament podem conjugar per matrius enteres) i el sorprenent teorema que diu que el grup $\\textup{SL}(n,\\mathbb{Z})$ per a $n\\geq 28$ s&#8217;obt\u00e9 com un quocient del grup $\\textup{SL}(2,\\mathbb{Z})$.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>La teoria de matrius enteres combina l&#8217;\u00e0lgebra lineal amb la teoria de grups i la teoria de nombres. Com el determinant de la inversa d&#8217;una matriu \u00e9s l&#8217;invers del determinant, per tal de tindre un grup, es consideren matrius amb determinant $\\pm 1$ ($\\textup{GL}(n,\\mathbb{Z}))$) o $1$ ($\\textup{SL}(n,\\mathbb{Z}))$). Algunes q\u00fcestions interessants que hi apareixen s\u00f3n si [&hellip;]<\/p>\n","protected":false},"author":54,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28],"tags":[22],"class_list":["post-647","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-roberto-rubio"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/647","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/users\/54"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/comments?post=647"}],"version-history":[{"count":1,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/647\/revisions"}],"predecessor-version":[{"id":648,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/647\/revisions\/648"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/media?parent=647"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/categories?post=647"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/tags?post=647"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}