{"id":1067,"date":"2014-03-06T17:59:01","date_gmt":"2014-03-06T17:59:01","guid":{"rendered":"http:\/\/www.faultorfeature.com\/?p=1067"},"modified":"2014-03-06T17:59:01","modified_gmt":"2014-03-06T17:59:01","slug":"inner-product-spaces-linear-algebra","status":"publish","type":"post","link":"https:\/\/www.faultorfeature.com\/?p=1067","title":{"rendered":"Inner Product Spaces (Linear Algebra)?"},"content":{"rendered":"<p><strong><i>Question by HIYA<\/i>: Inner Product Spaces (Linear Algebra)?<\/strong><\/p>\n<p>A vector space is valid on the interval (0, pi) with the inner product (f,g) in V. Consider the integral<br \/>\nS f(x)g(x) dx on the interval [0, pi]. Prove that cosx and sinx are orthogonal.<\/p>\n<p><strong>Best answer:<\/strong><\/p>\n<p><i>Answer by Lake R<\/i><br \/>You&#8217;re mangling the problem statement. What you are apparently asking about is a vector space of continuous functions on an interval with the usual inner product. <\/p>\n<p>Recall that two vectors are orthogonal if their inner product is zero. So just integrate. (cos(x), sin(x)) = <\/p>\n<p>?<br \/>\n? cos(x)sin(x) dx = \u00bdsin\u00b2(?) &#8211; \u00bdsin\u00b2(0) = 0.<br \/>\n0<\/p>\n<p>That&#8217;s it.<\/p>\n<p><strong>Give your answer to this question below!<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Question by HIYA: Inner Product Spaces (Linear Algebra)? A vector space is valid on the interval (0, pi) with the inner product (f,g) in V. Consider the integral S f(x)g(x) dx on the interval [0, pi]. Prove that cosx and sinx are orthogonal. Best answer: Answer by Lake RYou&#8217;re mangling the problem statement. What you [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8],"tags":[2752,2749,2751,16,2750],"class_list":["post-1067","post","type-post","status-publish","format-standard","hentry","category-recalls","tag-algebra","tag-inner","tag-linear","tag-product","tag-spaces"],"_links":{"self":[{"href":"https:\/\/www.faultorfeature.com\/index.php?rest_route=\/wp\/v2\/posts\/1067","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.faultorfeature.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.faultorfeature.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.faultorfeature.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.faultorfeature.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1067"}],"version-history":[{"count":0,"href":"https:\/\/www.faultorfeature.com\/index.php?rest_route=\/wp\/v2\/posts\/1067\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.faultorfeature.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1067"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.faultorfeature.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1067"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.faultorfeature.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1067"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}