{"id":48477,"date":"2025-11-23T13:04:16","date_gmt":"2025-11-23T13:04:16","guid":{"rendered":"https:\/\/idea.membrane.com\/songwriter\/?p=48477"},"modified":"2025-11-23T13:04:16","modified_gmt":"2025-11-23T13:04:16","slug":"transposition","status":"publish","type":"post","link":"https:\/\/kingarthur.com\/songwriter\/2025\/11\/23\/transposition\/","title":{"rendered":"Transposition"},"content":{"rendered":"<p><a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XVII\/Transposition.mp3\">Transposition.mp3<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XVII\/Transposition.mp4\">Transposition.mp4<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XVII\/Transposition-Pt-2.mp3\">Transposition-Pt-2.mp3<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XVII\/Transposition-Pt-2.mp4\">Transposition-Pt-2.mp4<\/a><br \/>\n<a href=\"http:\/\/kingarthur.com\/MegaEpix-Enormous\/multimedia\/XVII\/Transposition-intro.mp3\">Transposition-intro.mp3<\/a><\/p>\n<p>[Intro]<br \/>\nTransposition<br \/>\n(Changed condition)<\/p>\n<p>[Verse 1]<br \/>\nDo you believe<br \/>\n(Black is white)<br \/>\nCan you conceive<br \/>\n(That&#8217;s not right)<\/p>\n<p>[Chorus]<br \/>\nExclamation (Point!)<br \/>\nFormation (Adjoint)<br \/>\nSupposition<br \/>\n(Transposition)<\/p>\n<p>[Bridge]<br \/>\n(Changing your sign)<br \/>\nIn a changing time<\/p>\n<p>[Verse 2]<br \/>\nDo you think you know<br \/>\n(White is black)<br \/>\nWell, there ya go<br \/>\n(&#8230; wisdom lack)<\/p>\n<p>[Chorus]<br \/>\nExclamation (Point!)<br \/>\nFormation (Adjoint)<br \/>\nSupposition<br \/>\n(Transposition)<\/p>\n<p>[Bridge]<br \/>\nOverrule intuition<br \/>\n(Mathematician)<br \/>\n(Changing your sign)<br \/>\nIn a changing time<\/p>\n<p>[Outro]<br \/>\nExclamation (Point!)<br \/>\nFormation (Adjoint)<br \/>\nAlgebraic transposition<br \/>\n(Do you suppose)<br \/>\nMatrix transpose<br \/>\n(Flipping our lid)<br \/>\nYes&#8230; yes, we did<\/p>\n<p>ABOUT THE SONG<\/p>\n<div class=\"WaaZC\">\n<div class=\"rPeykc\" data-hveid=\"CE4QAQ\" data-ved=\"2ahUKEwi4nfr2uoaRAxWFKVkFHXTTOycQo_EKegQIThAB\"><span data-huuid=\"3161553363015300562\">In math, to &#8220;transpose&#8221; means to switch the rows and columns of a matrix or, in algebra, to move a term from one side of an equation to the other by changing its sign. <\/span><span data-huuid=\"3161553363015303131\">Transposing a matrix is often shown with a superscript &#8216;T&#8217; <span class=\"M5tQyf\">(<\/span><\/span>ATcap A to the cap T-th power \ud835\udc34\ud835\udc47<span data-huuid=\"3161553363015303131\"><span class=\"M5tQyf\">)<\/span> and involves flipping the matrix over its main diagonal. <\/span><span data-huuid=\"3161553363015301604\">In an equation, moving a term across the equals sign is a form of transposition that helps in solving for a variable. <\/span><br \/>\n<span data-huuid=\"3161553363015302646\"><span class=\"pjBG2e\" data-cid=\"b56d90e0-4718-43cb-bff1-3752437047ac\"><span class=\"UV3uM\">\u00a0<\/span><\/span><\/span><\/div>\n<\/div>\n<div class=\"WaaZC\">\n<div class=\"rPeykc uP58nb rWIipd\" role=\"heading\" aria-level=\"3\" data-hveid=\"CDYQAQ\" data-ved=\"2ahUKEwi4nfr2uoaRAxWFKVkFHXTTOycQo_EKegQINhAB\"><span data-huuid=\"3161553363015299592\"><strong>Matrix transpose<\/strong> <\/span><\/div>\n<\/div>\n<div class=\"WaaZC\">\n<ul data-hveid=\"CFYQAQ\" data-ved=\"2ahUKEwi4nfr2uoaRAxWFKVkFHXTTOycQm_YKegQIVhAB\">\n<li><span data-huuid=\"3161553363015299107\"><strong>What it is:<\/strong> <\/span><span data-huuid=\"3161553363015301676\">Switching the rows and columns of a matrix.<span class=\"pjBG2e\" data-cid=\"3565f6cf-fd69-4d03-a0fe-cbf2cc6dcba6\"><span class=\"UV3uM\">\u00a0<\/span><\/span><\/span>\n<div class=\"NPrrbc\" data-cid=\"3565f6cf-fd69-4d03-a0fe-cbf2cc6dcba6\" data-uuids=\"3161553363015299107,3161553363015301676\">\n<div class=\"BMebGe btku5b LwdV0e FR7ZSc OJeuxf\" tabindex=\"0\" role=\"button\" aria-label=\"View related links\" data-hveid=\"CFMQAQ\" data-ved=\"2ahUKEwi4nfr2uoaRAxWFKVkFHXTTOycQ3fYKegQIUxAB\">\n<div class=\"niO4u\"><\/div>\n<\/div>\n<\/div>\n<\/li>\n<li><span data-huuid=\"3161553363015302718\"><strong>How it works:<\/strong> <\/span><span data-huuid=\"3161553363015301191\">The element in the first row and first column of the original matrix becomes the element in the first row and first column of the new matrix. <\/span><span data-huuid=\"3161553363015299664\">The element in the first row and second column of the original becomes the element in the second row and first column of the new matrix, and so on.<span class=\"pjBG2e\" data-cid=\"a581d12f-1362-4cac-9caa-3af13de109c7\"><span class=\"UV3uM\">\u00a0<\/span><\/span><\/span>\n<div class=\"NPrrbc\" data-cid=\"a581d12f-1362-4cac-9caa-3af13de109c7\" data-uuids=\"3161553363015302718,3161553363015301191,3161553363015299664\">\n<div class=\"BMebGe btku5b LwdV0e FR7ZSc OJeuxf\" tabindex=\"0\" role=\"button\" aria-label=\"View related links\" data-hveid=\"CFIQAQ\" data-ved=\"2ahUKEwi4nfr2uoaRAxWFKVkFHXTTOycQ3fYKegQIUhAB\">\n<div class=\"niO4u\"><\/div>\n<\/div>\n<\/div>\n<\/li>\n<li><span data-huuid=\"3161553363015300706\"><strong>Result:<\/strong> <\/span><span data-huuid=\"3161553363015299179\">A<\/span>\n<div class=\"CM8kHf j86kh\" data-hveid=\"CE0QAQ\">\n<div data-expression=\"2 \\times 3\">\n<div tabindex=\"-1\" data-xpm-copy-root=\"\">\n<div>2\u00d732 cross 3<\/div>\n<p>2\u00d73<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><span data-huuid=\"3161553363015299179\">matrix will become a<\/span><img decoding=\"async\" loading=\"lazy\" role=\"presentation\" draggable=\"false\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAP\/\/\/wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==\" aria-hidden=\"true\" data-xpm-latex=\"3\\times 2\" data-csiid=\"pAoiabi7BoXT5NoP9KbvuQI_11\" data-atf=\"1\" \/><\/p>\n<div class=\"CM8kHf j86kh\" data-hveid=\"CE0QAg\">\n<div data-expression=\"3 \\times 2\">\n<div tabindex=\"-1\" data-xpm-copy-root=\"\">\n<div>3\u00d723 cross 2<\/div>\n<p>3\u00d72<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><span data-huuid=\"3161553363015299179\">matrix after transposing.<span class=\"pjBG2e\" data-cid=\"582c45e8-bfa4-4c88-b95d-852a768f8827\"><span class=\"UV3uM\">\u00a0<\/span><\/span><\/span><\/p>\n<div class=\"NPrrbc\" data-cid=\"582c45e8-bfa4-4c88-b95d-852a768f8827\" data-uuids=\"3161553363015300706,3161553363015299179\"><\/div>\n<\/li>\n<\/ul>\n<\/div>\n<div class=\"WaaZC\">\n<div class=\"rPeykc uP58nb rWIipd\" role=\"heading\" aria-level=\"3\" data-hveid=\"CDIQAQ\" data-ved=\"2ahUKEwi4nfr2uoaRAxWFKVkFHXTTOycQo_EKegQIMhAB\"><span data-huuid=\"3161553363015300221\"><strong>Algebraic transposition<\/strong> <\/span><\/div>\n<\/div>\n<div class=\"WaaZC\">\n<ul data-hveid=\"CEEQAQ\" data-ved=\"2ahUKEwi4nfr2uoaRAxWFKVkFHXTTOycQm_YKegQIQRAB\">\n<li style=\"list-style-type: none;\">\n<ul data-hveid=\"CEEQAQ\" data-ved=\"2ahUKEwi4nfr2uoaRAxWFKVkFHXTTOycQm_YKegQIQRAB\">\n<li>\n<div class=\"zMgcWd dSKvsb\" data-il=\"\">\n<div data-crb-p=\"\">\n<div class=\"xFTqob\">\n<div class=\"Gur8Ad\"><span data-huuid=\"3161553363015299736\"><strong>What it is:<\/strong> <\/span><\/div>\n<div class=\"vM0jzc\"><span data-huuid=\"3161553363015302305\">Moving a term from one side of an equation to the other by performing the inverse operation on both sides. <\/span><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<div id=\"pAoiabi7BoXT5NoP9KbvuQI__62\" class=\"bsmXxe\" role=\"none\">\n<ul>\n<li>\n<div class=\"zMgcWd dSKvsb\" data-il=\"\">\n<div data-crb-p=\"\">\n<div class=\"xFTqob\">\n<div class=\"Gur8Ad\"><span data-huuid=\"3161553363015299251\"><strong>How it works:<\/strong> <\/span><\/div>\n<div class=\"vM0jzc\"><span data-huuid=\"3161553363015301820\">When you move a term, you change its sign.\u00a0<\/span><span data-huuid=\"3161553363015300293\">For example, if you have<\/span><\/p>\n<div class=\"CM8kHf j86kh\" data-hveid=\"CIsBEAE\">\n<div data-expression=\"7x = 4x - 12\">\n<div tabindex=\"-1\" data-xpm-copy-root=\"\">\n<div>7x=4x\u2212127 x equals 4 x minus 12<\/div>\n<p>7\ud835\udc65=4\ud835\udc65\u221212<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><span data-huuid=\"3161553363015300293\"><span class=\"M5tQyf\">,<\/span> you can transpose the<\/span><img decoding=\"async\" loading=\"lazy\" role=\"presentation\" draggable=\"false\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAP\/\/\/wAAACH5BAEAAAAALAAAAAABAAEAAAICRAEAOw==\" aria-hidden=\"true\" data-xpm-latex=\"4x\" \/><\/p>\n<div class=\"CM8kHf j86kh\" data-hveid=\"CIsBEAI\">\n<div data-expression=\"4x\">\n<div tabindex=\"-1\" data-xpm-copy-root=\"\">\n<div>4&#215;4 x<\/div>\n<p>4\ud835\udc65<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p><span data-huuid=\"3161553363015300293\">by subtracting it from both sides:<\/span><\/p>\n<div class=\"CM8kHf j86kh\" data-hveid=\"CIsBEAM\">\n<div data-expression=\"7x - 4x = -12\">\n<div tabindex=\"-1\" data-xpm-copy-root=\"\">\n<div>7x\u22124x=-127 x minus 4 x equals negative 12<\/div>\n<p>7\ud835\udc65\u22124\ud835\udc65=\u221212<span data-huuid=\"3161553363015300293\">\u00a0<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/li>\n<\/ul>\n<\/div>\n<div id=\"pAoiabi7BoXT5NoP9KbvuQI__68\" class=\"bsmXxe\" role=\"none\">\n<ul>\n<li>\n<div class=\"zMgcWd dSKvsb\" data-il=\"\">\n<div data-crb-p=\"\">\n<div class=\"xFTqob\">\n<div class=\"Gur8Ad\"><span data-huuid=\"3161553363015301335\"><strong>Result:<\/strong> <\/span><\/div>\n<div class=\"vM0jzc\"><span data-huuid=\"3161553363015299808\">This helps isolate variables to solve the equation.\u00a0<\/span><span data-huuid=\"3161553363015302377\">In the example, this becomes<\/span><\/p>\n<div class=\"CM8kHf j86kh\" data-hveid=\"CI0BEAE\">\n<div data-expression=\"3x = -12\">\n<div tabindex=\"-1\" data-xpm-copy-root=\"\">\n<div>3x=-123 x equals negative 12<\/div>\n<p>3\ud835\udc65=\u221212<span data-huuid=\"3161553363015302377\"><span class=\"pjBG2e\" data-cid=\"c876e670-e243-4f89-802a-8b7f6b7ed31c\"><span class=\"UV3uM\">\u00a0<\/span><\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"NPrrbc\" data-cid=\"c876e670-e243-4f89-802a-8b7f6b7ed31c\" data-uuids=\"3161553363015299736,3161553363015302305,3161553363015299251,3161553363015301820,3161553363015300293,3161553363015301335,3161553363015299808,3161553363015302377\">\n<div class=\"BMebGe btku5b LwdV0e FR7ZSc OJeuxf\" tabindex=\"0\" role=\"button\" aria-label=\"View related links\" data-hveid=\"CI0BEAI\" data-ved=\"2ahUKEwi4nfr2uoaRAxWFKVkFHXTTOycQ3fYKegUIjQEQAg\">\n<div class=\"niO4u\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p><strong>From the album &#8220;<a href=\"\/songwriter\/tag\/lulu\/\">Lulu<\/a>&#8220;<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Transposition.mp3 Transposition.mp4 Transposition-Pt-2.mp3 Transposition-Pt-2.mp4 Transposition-intro.mp3 [Intro] Transposition (Changed condition) [Verse 1] Do you believe (Black is white) Can you conceive (That&#8217;s not right) [Chorus] Exclamation (Point!) Formation (Adjoint) Supposition (Transposition) [Bridge] (Changing your sign) In a changing time [Verse 2] Do you think you know (White is black) Well, there ya go (&#8230; wisdom lack) [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","footnotes":""},"categories":[3,9,14],"tags":[4183],"class_list":["post-48477","post","type-post","status-publish","format-standard","hentry","category-4d-music","category-daniel","category-lyrics","tag-lulu"],"_links":{"self":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/48477","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/comments?post=48477"}],"version-history":[{"count":6,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/48477\/revisions"}],"predecessor-version":[{"id":48502,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/posts\/48477\/revisions\/48502"}],"wp:attachment":[{"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/media?parent=48477"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/categories?post=48477"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kingarthur.com\/songwriter\/wp-json\/wp\/v2\/tags?post=48477"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}