{"id":157,"date":"2023-07-20T15:26:55","date_gmt":"2023-07-20T14:26:55","guid":{"rendered":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/?p=157"},"modified":"2023-07-21T06:16:34","modified_gmt":"2023-07-21T05:16:34","slug":"change-of-basis-of-a-linear-map","status":"publish","type":"post","link":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/","title":{"rendered":"Change of basis of a linear map"},"content":{"rendered":"<h3>1. Coordinate maps<\/h3>\n<p>consider a random vector <strong><em>a<\/em><\/strong>. If the values of every entry are explicitly given, one could naturally identify it as a vector under the orthonormal basis. However, it could also been understood as the <em>coordinate vector<\/em>, which represents a vector under another basis by a <em>coordinate map<\/em>:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"1375\" height=\"46\" class=\"alignnone size-full wp-image-158\" src=\"http:\/\/blogs.imperial.ac.uk\/cocteaupedia\/files\/2023\/07\/equation1-1.png\" alt=\"\" \/><\/p>\n<h3>2. Change of basis of a linear map<\/h3>\n<p>Now we consider a linear map (represented by a matrix) A. It could be interpreted \u00a0as:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"230\" height=\"21\" class=\"alignnone size-full wp-image-162\" src=\"http:\/\/blogs.imperial.ac.uk\/cocteaupedia\/files\/2023\/07\/CodeCogsEqn-2.gif\" alt=\"\" \/><\/p>\n<p>What if we want to change the basis of the objective vector space of <em>f<\/em> ? The following relation is obvious, if we want to find a matrix <em>A&#8217;<\/em> representing the map after change of basis:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"462\" height=\"21\" class=\"alignnone size-full wp-image-165\" src=\"http:\/\/blogs.imperial.ac.uk\/cocteaupedia\/files\/2023\/07\/CodeCogsEqn-3.gif\" alt=\"\" \/><\/p>\n<p>Where <em>P<\/em> is defined as a matrix that perform this basis change.<\/p>\n<p><strong>[Literature: Andre Lukas, Lecture note on Vectors and Matrices, University of Oxford]<\/strong><\/p>\n<h3>3. The invariant map<\/h3>\n<p>Suppose we have a map that is invariant under any basis change, that is:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"240\" height=\"21\" class=\"alignnone size-full wp-image-167\" src=\"http:\/\/blogs.imperial.ac.uk\/cocteaupedia\/files\/2023\/07\/CodeCogsEqn-4.gif\" alt=\"\" \/><\/p>\n<p>In other words, we would like to find an operator that commutes with any other operator on the same vector space <em>V<\/em>. Suppose now we have a vector <strong><em>x<\/em><\/strong> in <em>V<\/em>. We would like to find a non-trivial linear functional on <em><strong>x<\/strong><\/em>, so that we can define a linear map:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"343\" height=\"19\" class=\"alignnone size-full wp-image-169\" src=\"http:\/\/blogs.imperial.ac.uk\/cocteaupedia\/files\/2023\/07\/CodeCogsEqn-5.gif\" alt=\"\" \/><\/p>\n<p>This is possible, for a functional in a <em>n <\/em>dimensional space can be express in to an <em>(1 x n)<\/em> matrix, so the left hand side can be expressed as <em>(nx1)(1xn)(nx1)<\/em> corresponding to <strong><em>v<\/em><\/strong>, <em>f<\/em>, and <strong><em>x<\/em> <\/strong>respectively, and the former 2 combined and form a matrix. ( <strong><em>My reference mentioned &#8221; Axiom of choice&#8221; with respect to finding non-trivial functional, and yet I have not understood it perfectly<\/em><\/strong>)<\/p>\n<p>Then, the commutation relation implies:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"356\" height=\"19\" class=\"alignnone size-full wp-image-170\" src=\"http:\/\/blogs.imperial.ac.uk\/cocteaupedia\/files\/2023\/07\/CodeCogsEqn-6.gif\" alt=\"\" \/><\/p>\n<p>Note that <em>f(T<strong>x<\/strong>)<\/em>, according to our pervious argument, should exist and independent on <strong><em>v<\/em><\/strong>. Thus, what we are doing consequently is that we have constructed linear maps <em>P<\/em> according to our need (that is, the vector <strong><em>v<\/em><\/strong>). In other words, we can assign every vector <strong><em>v<\/em><\/strong> in <em>V<\/em> a matrix <em>P<\/em> and they have to satisfy (6).<\/p>\n<p>Then this inplies:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" width=\"234\" height=\"44\" class=\"alignnone size-full wp-image-173\" src=\"http:\/\/blogs.imperial.ac.uk\/cocteaupedia\/files\/2023\/07\/CodeCogsEqn-7.gif\" alt=\"\" \/><\/p>\n<p><em>i.e.<\/em> <strong><em>T is the scalar multiple of \u00a0the identity<\/em><\/strong>.<\/p>\n<p><strong>[Literature: Robert Isreal, https:\/\/math.stackexchange.com\/questions\/27808\/a-linear-operator-commuting-with-all-such-operators-is-a-scalar-multiple-of-the]<\/strong><\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>1. Coordinate maps consider a random vector a. If the values of every entry are explicitly given, one could naturally identify it as a vector under the orthonormal basis. However, it could also been understood as the coordinate vector, which represents a vector under another basis by a coordinate map: 2. Change of basis of [&hellip;]<\/p>\n","protected":false},"author":1741,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[],"class_list":["post-157","post","type-post","status-publish","format-standard","hentry","category-linear-algebra"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Change of basis of a linear map - Cocteaupedia<\/title>\n<meta name=\"description\" content=\"Identity map, Change of basis\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/\" \/>\n<meta property=\"og:locale\" content=\"en_GB\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Change of basis of a linear map - Cocteaupedia\" \/>\n<meta property=\"og:description\" content=\"Identity map, Change of basis\" \/>\n<meta property=\"og:url\" content=\"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/\" \/>\n<meta property=\"og:site_name\" content=\"Cocteaupedia\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-20T14:26:55+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-07-21T05:16:34+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/blogs.imperial.ac.uk\/cocteaupedia\/files\/2023\/07\/equation1-1.png\" \/>\n<meta name=\"author\" content=\"Cocteau Huang\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Cocteau Huang\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimated reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/2023\\\/07\\\/20\\\/change-of-basis-of-a-linear-map\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/2023\\\/07\\\/20\\\/change-of-basis-of-a-linear-map\\\/\"},\"author\":{\"name\":\"Cocteau Huang\",\"@id\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/#\\\/schema\\\/person\\\/d57ea00ff9e768fd4a27699d30e027c5\"},\"headline\":\"Change of basis of a linear map\",\"datePublished\":\"2023-07-20T14:26:55+00:00\",\"dateModified\":\"2023-07-21T05:16:34+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/2023\\\/07\\\/20\\\/change-of-basis-of-a-linear-map\\\/\"},\"wordCount\":357,\"commentCount\":0,\"image\":{\"@id\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/2023\\\/07\\\/20\\\/change-of-basis-of-a-linear-map\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/files\\\/2023\\\/07\\\/equation1-1.png\",\"articleSection\":[\"Linear Algebra\"],\"inLanguage\":\"en-GB\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/2023\\\/07\\\/20\\\/change-of-basis-of-a-linear-map\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/2023\\\/07\\\/20\\\/change-of-basis-of-a-linear-map\\\/\",\"url\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/2023\\\/07\\\/20\\\/change-of-basis-of-a-linear-map\\\/\",\"name\":\"Change of basis of a linear map - Cocteaupedia\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/2023\\\/07\\\/20\\\/change-of-basis-of-a-linear-map\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/2023\\\/07\\\/20\\\/change-of-basis-of-a-linear-map\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/files\\\/2023\\\/07\\\/equation1-1.png\",\"datePublished\":\"2023-07-20T14:26:55+00:00\",\"dateModified\":\"2023-07-21T05:16:34+00:00\",\"author\":{\"@id\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/#\\\/schema\\\/person\\\/d57ea00ff9e768fd4a27699d30e027c5\"},\"description\":\"Identity map, Change of basis\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/2023\\\/07\\\/20\\\/change-of-basis-of-a-linear-map\\\/#breadcrumb\"},\"inLanguage\":\"en-GB\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/2023\\\/07\\\/20\\\/change-of-basis-of-a-linear-map\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-GB\",\"@id\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/2023\\\/07\\\/20\\\/change-of-basis-of-a-linear-map\\\/#primaryimage\",\"url\":\"http:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/files\\\/2023\\\/07\\\/equation1-1.png\",\"contentUrl\":\"http:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/files\\\/2023\\\/07\\\/equation1-1.png\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/2023\\\/07\\\/20\\\/change-of-basis-of-a-linear-map\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Change of basis of a linear map\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/#website\",\"url\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/\",\"name\":\"Cocteaupedia\",\"description\":\"Notes in Theoretical Physics and Maths\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-GB\"},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/#\\\/schema\\\/person\\\/d57ea00ff9e768fd4a27699d30e027c5\",\"name\":\"Cocteau Huang\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-GB\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/86d23a25bc24e1ee9655f0b3d54afae109abdd6c1a56430c44bf0380db8bc5f8?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/86d23a25bc24e1ee9655f0b3d54afae109abdd6c1a56430c44bf0380db8bc5f8?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/86d23a25bc24e1ee9655f0b3d54afae109abdd6c1a56430c44bf0380db8bc5f8?s=96&d=mm&r=g\",\"caption\":\"Cocteau Huang\"},\"url\":\"https:\\\/\\\/blogs.imperial.ac.uk\\\/cocteaupedia\\\/author\\\/yh1721\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Change of basis of a linear map - Cocteaupedia","description":"Identity map, Change of basis","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/","og_locale":"en_GB","og_type":"article","og_title":"Change of basis of a linear map - Cocteaupedia","og_description":"Identity map, Change of basis","og_url":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/","og_site_name":"Cocteaupedia","article_published_time":"2023-07-20T14:26:55+00:00","article_modified_time":"2023-07-21T05:16:34+00:00","og_image":[{"url":"http:\/\/blogs.imperial.ac.uk\/cocteaupedia\/files\/2023\/07\/equation1-1.png","type":"","width":"","height":""}],"author":"Cocteau Huang","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Cocteau Huang","Estimated reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/#article","isPartOf":{"@id":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/"},"author":{"name":"Cocteau Huang","@id":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/#\/schema\/person\/d57ea00ff9e768fd4a27699d30e027c5"},"headline":"Change of basis of a linear map","datePublished":"2023-07-20T14:26:55+00:00","dateModified":"2023-07-21T05:16:34+00:00","mainEntityOfPage":{"@id":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/"},"wordCount":357,"commentCount":0,"image":{"@id":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/#primaryimage"},"thumbnailUrl":"http:\/\/blogs.imperial.ac.uk\/cocteaupedia\/files\/2023\/07\/equation1-1.png","articleSection":["Linear Algebra"],"inLanguage":"en-GB","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/","url":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/","name":"Change of basis of a linear map - Cocteaupedia","isPartOf":{"@id":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/#website"},"primaryImageOfPage":{"@id":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/#primaryimage"},"image":{"@id":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/#primaryimage"},"thumbnailUrl":"http:\/\/blogs.imperial.ac.uk\/cocteaupedia\/files\/2023\/07\/equation1-1.png","datePublished":"2023-07-20T14:26:55+00:00","dateModified":"2023-07-21T05:16:34+00:00","author":{"@id":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/#\/schema\/person\/d57ea00ff9e768fd4a27699d30e027c5"},"description":"Identity map, Change of basis","breadcrumb":{"@id":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/#breadcrumb"},"inLanguage":"en-GB","potentialAction":[{"@type":"ReadAction","target":["https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/"]}]},{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/#primaryimage","url":"http:\/\/blogs.imperial.ac.uk\/cocteaupedia\/files\/2023\/07\/equation1-1.png","contentUrl":"http:\/\/blogs.imperial.ac.uk\/cocteaupedia\/files\/2023\/07\/equation1-1.png"},{"@type":"BreadcrumbList","@id":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/2023\/07\/20\/change-of-basis-of-a-linear-map\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/"},{"@type":"ListItem","position":2,"name":"Change of basis of a linear map"}]},{"@type":"WebSite","@id":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/#website","url":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/","name":"Cocteaupedia","description":"Notes in Theoretical Physics and Maths","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-GB"},{"@type":"Person","@id":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/#\/schema\/person\/d57ea00ff9e768fd4a27699d30e027c5","name":"Cocteau Huang","image":{"@type":"ImageObject","inLanguage":"en-GB","@id":"https:\/\/secure.gravatar.com\/avatar\/86d23a25bc24e1ee9655f0b3d54afae109abdd6c1a56430c44bf0380db8bc5f8?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/86d23a25bc24e1ee9655f0b3d54afae109abdd6c1a56430c44bf0380db8bc5f8?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/86d23a25bc24e1ee9655f0b3d54afae109abdd6c1a56430c44bf0380db8bc5f8?s=96&d=mm&r=g","caption":"Cocteau Huang"},"url":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/author\/yh1721\/"}]}},"_links":{"self":[{"href":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/wp-json\/wp\/v2\/posts\/157","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/wp-json\/wp\/v2\/users\/1741"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/wp-json\/wp\/v2\/comments?post=157"}],"version-history":[{"count":8,"href":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/wp-json\/wp\/v2\/posts\/157\/revisions"}],"predecessor-version":[{"id":175,"href":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/wp-json\/wp\/v2\/posts\/157\/revisions\/175"}],"wp:attachment":[{"href":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/wp-json\/wp\/v2\/media?parent=157"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/wp-json\/wp\/v2\/categories?post=157"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.imperial.ac.uk\/cocteaupedia\/wp-json\/wp\/v2\/tags?post=157"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}