{"id":232,"date":"2024-04-28T21:52:20","date_gmt":"2024-04-28T21:52:20","guid":{"rendered":"https:\/\/src.cikeys.com\/2024\/?page_id=232"},"modified":"2024-04-28T22:43:31","modified_gmt":"2024-04-28T22:43:31","slug":"dual-complex-a-look-at-dual-and-complex-numbers-with-matrix-representations","status":"publish","type":"page","link":"https:\/\/src.cikeys.com\/2024\/conference-schedule\/poster-presentations\/poster-presentations-session-1\/dual-complex-a-look-at-dual-and-complex-numbers-with-matrix-representations\/","title":{"rendered":"Dual Complex: A Look at Dual and Complex Numbers with Matrix Representations"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">Michael Nunley, &amp; Dr. Ivona Grzegorczyk<\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<p class=\"wp-block-paragraph\">We explore the fascinating world of dual numbers, where a new imaginary unit, \u03b5, satisfies \u03b5\u00b2 = 0. We compare them with the familiar complex numbers, where the imaginary unit, i, satisfies i\u00b2 = -1.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We delve into:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Definitions and basic operations of dual and complex numbers.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Unveiling the surprising properties of \u03b5 compared to i.<\/li>\n\n\n\n<li>Understanding how these number systems go beyond the real numbers.<\/li>\n\n\n\n<li>Unveiling the power of matrix representations:<\/li>\n\n\n\n<li>Visualizing complex numbers as 2&#215;2 matrices:<\/li>\n\n\n\n<li>We represent a complex number a + bi as a 2&#215;2 matrix: [[a, b], [-b, a]]<\/li>\n\n\n\n<li>Representing dual numbers with matrices for efficient calculations:<\/li>\n\n\n\n<li>A dual number x + y\u03b5 corresponds to the matrix: [[x,y], [0, x]] where \u03b5\u00b2 = 0.<\/li>\n\n\n\n<li>We discuss the structure and surprises arising when combining these two fields.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Join us on a journey to unlock the secrets of these unique number systems and discover a new way to represent the mathematical world, with the added power of matrix visualization.<\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<p class=\"wp-block-paragraph\"><strong><a href=\"https:\/\/src.cikeys.com\/2024\/conference-schedule\/poster-presentations\/\">Poster Presentation<\/a><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/src.cikeys.com\/2024\/conference-schedule\/poster-presentations\/poster-presentations-session-1\/\">Session 1<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">9:15am\u00a0<strong>\u2013<\/strong>\u00a010:30am<br>Grand Salon<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Mathematics<\/strong><\/p>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Michael Nunley, &amp; Dr. Ivona Grzegorczyk We explore the fascinating world of dual numbers, where a new imaginary unit, \u03b5, satisfies \u03b5\u00b2 = 0. We compare them with the familiar complex numbers, where the imaginary unit, i, satisfies i\u00b2 = -1. We delve into: Definitions and basic operations of dual and complex numbers. Join us [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":45,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"categories":[5,6],"tags":[31],"class_list":["post-232","page","type-page","status-publish","hentry","category-poster-presentations","category-session-1","tag-mathematics","post"],"_links":{"self":[{"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/pages\/232","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/comments?post=232"}],"version-history":[{"count":2,"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/pages\/232\/revisions"}],"predecessor-version":[{"id":408,"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/pages\/232\/revisions\/408"}],"up":[{"embeddable":true,"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/pages\/45"}],"wp:attachment":[{"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/media?parent=232"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/categories?post=232"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/src.cikeys.com\/2024\/wp-json\/wp\/v2\/tags?post=232"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}