{"id":70,"date":"2011-09-01T08:13:39","date_gmt":"2011-09-01T08:13:39","guid":{"rendered":"http:\/\/florian-roemer.de\/blog\/?p=70"},"modified":"2011-09-01T08:15:14","modified_gmt":"2011-09-01T08:15:14","slug":"even-more-algebra-fun","status":"publish","type":"post","link":"https:\/\/florian-roemer.de\/blog\/even-more-algebra-fun\/","title":{"rendered":"Even more algebra fun"},"content":{"rendered":"<p>I just realized that there is an even more general version of the rules for quadratic forms I<a title=\"Fun with algebra\" href=\"http:\/\/florian-roemer.de\/blog\/?p=41\"> posted recently<\/a>:<\/p>\n<p>$${\\rm trace}\\left(\\ma{A} \\cdot \\ma{X} \\cdot \\ma{R} \\cdot \\ma{X}^{\\rm H} \\cdot \\ma{B}^{\\rm H}\\right) = {\\rm vec}\\left(\\ma{X}\\right)^{\\rm H} \\cdot \\left( \\ma{R}^{\\rm T} \\otimes \\ma{B}^{\\rm H} \\cdot \\ma{A} \\right) \\cdot {\\rm vec}\\left(\\ma{X}\\right) $$<\/p>\n<p>Enjoy!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I just realized that there is an even more general version of the rules for quadratic forms I posted recently: $${\\rm trace}\\left(\\ma{A} \\cdot \\ma{X} \\cdot \\ma{R} \\cdot \\ma{X}^{\\rm H} \\cdot \\ma{B}^{\\rm H}\\right) = {\\rm vec}\\left(\\ma{X}\\right)^{\\rm H} \\cdot \\left( \\ma{R}^{\\rm T} \\otimes \\ma{B}^{\\rm H} \\cdot \\ma{A} \\right) \\cdot {\\rm vec}\\left(\\ma{X}\\right) $$ Enjoy!<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3],"tags":[4,5,7],"_links":{"self":[{"href":"https:\/\/florian-roemer.de\/blog\/wp-json\/wp\/v2\/posts\/70"}],"collection":[{"href":"https:\/\/florian-roemer.de\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/florian-roemer.de\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/florian-roemer.de\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/florian-roemer.de\/blog\/wp-json\/wp\/v2\/comments?post=70"}],"version-history":[{"count":3,"href":"https:\/\/florian-roemer.de\/blog\/wp-json\/wp\/v2\/posts\/70\/revisions"}],"predecessor-version":[{"id":75,"href":"https:\/\/florian-roemer.de\/blog\/wp-json\/wp\/v2\/posts\/70\/revisions\/75"}],"wp:attachment":[{"href":"https:\/\/florian-roemer.de\/blog\/wp-json\/wp\/v2\/media?parent=70"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/florian-roemer.de\/blog\/wp-json\/wp\/v2\/categories?post=70"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/florian-roemer.de\/blog\/wp-json\/wp\/v2\/tags?post=70"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}