{"id":14655,"date":"2022-05-20T19:58:10","date_gmt":"2022-05-20T23:58:10","guid":{"rendered":"https:\/\/carleton.ca\/scs\/?page_id=14655"},"modified":"2026-06-09T14:38:32","modified_gmt":"2026-06-09T18:38:32","slug":"tr-29-another-addendum-to-kroneckers-theory-of-pencils","status":"publish","type":"page","link":"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1983\/tr-29-another-addendum-to-kroneckers-theory-of-pencils\/","title":{"rendered":"TR-29: Another Addendum to Kronecker&#8217;s Theory of Pencils"},"content":{"rendered":"\n<section class=\"w-screen px-6 cu-section cu-section--white ml-offset-center md:px-8 lg:px-14\">\n    <div class=\"space-y-6 cu-max-w-child-5xl  md:space-y-10 cu-prose-first-last\">\n\n            <div class=\"cu-textmedia flex flex-col lg:flex-row mx-auto gap-6 md:gap-10 my-6 md:my-12 first:mt-0 max-w-5xl\">\n        <div class=\"justify-start cu-textmedia-content cu-prose-first-last\" style=\"flex: 0 0 100%;\">\n            <header class=\"font-light prose-xl cu-pageheader md:prose-2xl cu-component-updated cu-prose-first-last\">\n                                    <h1 class=\"cu-prose-first-last font-semibold !mt-2 mb-4 md:mb-6 relative after:absolute after:h-px after:bottom-0 after:bg-cu-red after:left-px text-3xl md:text-4xl lg:text-5xl lg:leading-[3.5rem] pb-5 after:w-10 text-cu-black-700 not-prose\">\n                        TR-29: Another Addendum to Kronecker&#8217;s Theory of Pencils\n                    <\/h1>\n                \n                                \n                            <\/header>\n\n                    <\/div>\n\n            <\/div>\n\n    <\/div>\n<\/section>\n\n\n\n<p>Carleton University<br><a href=\"https:\/\/carleton.ca\/scs\/research\/scs-technical-reports\/technical-reports-1983\/\">Technical Report<\/a>\u00a0<strong>TR-29<\/strong><br>August 1983<\/p>\n\n\n\n<h2 id=\"another-addendum-to-kroneckers-theory-of-pencils\" class=\"wp-block-heading\">Another Addendum to Kronecker\u2019s Theory of Pencils<\/h2>\n\n\n\n<p>M.D. Atkinson<\/p>\n\n\n\n<h3 id=\"abstract\" class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<p>A classical theory due to Kronecker and Weierstrass shows how to decide when two pairs of matrices are equivalent under multiplication by non-singular matrices. Recent work in algebraic computational complexity has demanded a broader definition of equivalence. The classical theory is here extended to the new definition and illustrated by a result on pairs of 3 x 3 matrices: \u2013 with the new definition there are only a finite number of inequivalent pairs of 3 x 3 matrices.<\/p>\n\n\n\n<h3 id=\"download\" class=\"wp-block-heading\">Download<\/h3>\n\n\n\n<p><a href=\"https:\/\/carleton.ca\/scs\/wp-content\/uploads\/sites\/260\/TR-29.pdf\">TR-29.pdf<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Carleton UniversityTechnical Report\u00a0TR-29August 1983 Another Addendum to Kronecker\u2019s Theory of Pencils M.D. Atkinson Abstract A classical theory due to Kronecker and Weierstrass shows how to decide when two pairs of matrices are equivalent under multiplication by non-singular matrices. Recent work in algebraic computational complexity has demanded a broader definition of equivalence. The classical theory is [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":11785,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_cu_dining_location_slug":"","footnotes":"","_links_to":"","_links_to_target":""},"cu_page_type":[88],"class_list":["post-14655","page","type-page","status-publish","hentry","cu_page_type-technical-report"],"acf":{"cu_post_thumbnail":""},"_links":{"self":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14655","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/comments?post=14655"}],"version-history":[{"count":2,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14655\/revisions"}],"predecessor-version":[{"id":24568,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/14655\/revisions\/24568"}],"up":[{"embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/pages\/11785"}],"wp:attachment":[{"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/media?parent=14655"}],"wp:term":[{"taxonomy":"cu_page_type","embeddable":true,"href":"https:\/\/carleton.ca\/scs\/wp-json\/wp\/v2\/cu_page_type?post=14655"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}