{"id":2711,"date":"2023-07-21T01:48:22","date_gmt":"2023-07-21T01:48:22","guid":{"rendered":"https:\/\/statorials.org\/tr\/rdeki-carpimlar\/"},"modified":"2023-07-21T01:48:22","modified_gmt":"2023-07-21T01:48:22","slug":"rdeki-carpimlar","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/rdeki-carpimlar\/","title":{"rendered":"R&#39;de \u00e7apraz \u00e7arp\u0131m nas\u0131l hesaplan\u0131r"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">(A <sub>1<\/sub> , A <sub>2<\/sub> , A <sub>3<\/sub> ) elemanlar\u0131na sahip A vekt\u00f6r\u00fcm\u00fcz ve (B <sub>1<\/sub> , B <sub>2<\/sub> , B <sub>3<\/sub> ) elemanlar\u0131na sahip bir B vekt\u00f6r\u00fcm\u00fcz oldu\u011funu varsayarak, bu iki vekt\u00f6r\u00fcn \u00e7apraz \u00e7arp\u0131m\u0131n\u0131 a\u015fa\u011f\u0131daki \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00c7apraz \u00e7arp\u0131m<\/strong> = [(A <sub>2<\/sub> *B <sub>3<\/sub> ) \u2013 (A <sub>3<\/sub> *B <sub>2<\/sub> ), (A <sub>3<\/sub> *B <sub>1<\/sub> ) \u2013 (A <sub>1<\/sub> *B <sub>3<\/sub> ), (A <sub>1<\/sub> *B <sub>2<\/sub> ) \u2013 (A <sub>2<\/sub> *B <sub>1<\/sub> )]<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u00d6rne\u011fin a\u015fa\u011f\u0131daki vekt\u00f6rlere sahip oldu\u011fumuzu varsayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Vekt\u00f6r A: (1, 2, 3)<\/span><\/li>\n<li> <span style=\"color: #000000;\">Vekt\u00f6r B: (4, 5, 6)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Bu vekt\u00f6rlerin \u00e7apraz \u00e7arp\u0131m\u0131n\u0131 \u015fu \u015fekilde hesaplayabiliriz:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00c7apraz \u00e7arp\u0131m = [(A <sub>2<\/sub> *B <sub>3<\/sub> ) \u2013 (A <sub>3<\/sub> *B <sub>2<\/sub> ), (A <sub>3<\/sub> *B <sub>1<\/sub> ) \u2013 (A <sub>1<\/sub> *B <sub>3<\/sub> ), (A <sub>1<\/sub> *B <sub>2<\/sub> ) \u2013 (A <sub>2<\/sub> *B <sub>1<\/sub> )]<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00c7apraz \u00e7arp\u0131m = [(2*6) \u2013 (3*5), (3*4) \u2013 (1*6), (1*5) \u2013 (2*4)]<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00c7apraz \u00e7arp\u0131m = (-3, 6, -3)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">R&#8217;deki iki vekt\u00f6r\u00fcn \u00e7apraz \u00e7arp\u0131m\u0131n\u0131 hesaplamak i\u00e7in iki y\u00f6ntemden birini kullanabilirsiniz:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Y\u00f6ntem 1: pracma paketinin cross() i\u015flevini kullan\u0131n<\/strong><\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">library<\/span> (pracma)\n  \n<span style=\"color: #008080;\">#calculate cross product of vectors A and B\n<\/span>cross(A, B)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>Y\u00f6ntem 2: Kendi i\u015flevinizi tan\u0131mlay\u0131n<\/strong><\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define function to calculate cross product<\/span> \ncross &lt;- <span style=\"color: #008000;\">function<\/span> (x, y, i=1:3) {\n  create3D &lt;- <span style=\"color: #008000;\">function<\/span> (x) <span style=\"color: #3366ff;\">head<\/span> (c(x, <span style=\"color: #3366ff;\">rep<\/span> (0, 3)), 3)\n  x &lt;- create3D(x)\n  y &lt;- create3D(y)\n  j &lt;- <span style=\"color: #008000;\">function<\/span> (i) (i-1) <span style=\"color: #800080;\">%%<\/span> 3+1\n  <span style=\"color: #008000;\">return<\/span> (x[j(i+1)]*y[j(i+2)] - x[j(i+2)]*y[j(i+1)])\n}\n\n<span style=\"color: #008080;\">#calculate cross product\n<\/span>cross(A, B)<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki \u00f6rnekler her y\u00f6ntemin pratikte nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6stermektedir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: pracma paketinin cross() fonksiyonunu kullan\u0131n<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, iki vekt\u00f6r aras\u0131ndaki \u00e7apraz \u00e7arp\u0131m\u0131 hesaplamak i\u00e7in <a href=\"https:\/\/cran.r-project.org\/web\/packages\/pracma\/index.html\" target=\"_blank\" rel=\"noopener\">pracma<\/a> paketindeki <strong>cross()<\/strong> i\u015flevinin nas\u0131l kullan\u0131laca\u011f\u0131n\u0131 g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">library<\/span> (pracma)\n  \n<span style=\"color: #008080;\">#definevectors\n<\/span>A &lt;- c(1, 2, 3)\nB &lt;- c(4, 5, 6)\n  \n<span style=\"color: #008080;\">#calculate cross product\n<\/span>cross(A, B)\n\n[1] -3 6 -3\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u00c7apraz \u00e7arp\u0131m <strong>(-3, 6, -3)<\/strong> olur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, daha \u00f6nce manuel olarak hesaplad\u0131\u011f\u0131m\u0131z \u00e7apraz \u00e7arp\u0131ma kar\u015f\u0131l\u0131k gelir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Kendi i\u015flevinizi tan\u0131mlay\u0131n<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, iki vekt\u00f6r aras\u0131ndaki \u00e7apraz \u00e7arp\u0131m\u0131 hesaplamak i\u00e7in kendi fonksiyonunuzu nas\u0131l tan\u0131mlayaca\u011f\u0131n\u0131z\u0131 g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#define function to calculate cross product<\/span> \ncross &lt;- <span style=\"color: #008000;\">function<\/span> (x, y, i=1:3) {\n  create3D &lt;- <span style=\"color: #008000;\">function<\/span> (x) <span style=\"color: #3366ff;\">head<\/span> (c(x, <span style=\"color: #3366ff;\">rep<\/span> (0, 3)), 3)\n  x &lt;- create3D(x)\n  y &lt;- create3D(y)\n  j &lt;- <span style=\"color: #008000;\">function<\/span> (i) (i-1) <span style=\"color: #800080;\">%%<\/span> 3+1\n  <span style=\"color: #008000;\">return<\/span> (x[j(i+1)]*y[j(i+2)] - x[j(i+2)]*y[j(i+1)])\n}\n\n<span style=\"color: #008080;\">#definevectors\n<\/span>A &lt;- c(1, 2, 3)\nB &lt;- c(4, 5, 6)\n\n<span style=\"color: #008080;\">#calculate cross product\n<\/span>cross(A, B)\n\n[1] -3 6 -3\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u00c7apraz \u00e7arp\u0131m <strong>(-3, 6, -3)<\/strong> olur.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu, \u00f6nceki \u00f6rnekte hesaplad\u0131\u011f\u0131m\u0131z \u00e7apraz \u00e7arp\u0131ma kar\u015f\u0131l\u0131k gelir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Ek kaynaklar<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki e\u011fitimlerde R&#8217;de di\u011fer ortak g\u00f6revlerin nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/tr\/rdeki-nokta-carpim\/\" target=\"_blank\" rel=\"noopener\">R&#8217;de nokta \u00e7arp\u0131m nas\u0131l hesaplan\u0131r<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/rdeki-kimlik-matrisi\/\" target=\"_blank\" rel=\"noopener\">R&#8217;de kimlik matrisi nas\u0131l olu\u015fturulur<\/a><br \/> <a href=\"https:\/\/statorials.org\/tr\/rde-bos-bir-matris-olusturun\/\" target=\"_blank\" rel=\"noopener\">R&#8217;de bo\u015f bir matris nas\u0131l olu\u015fturulur<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>(A 1 , A 2 , A 3 ) elemanlar\u0131na sahip A vekt\u00f6r\u00fcm\u00fcz ve (B 1 , B 2 , B 3 ) elemanlar\u0131na sahip bir B vekt\u00f6r\u00fcm\u00fcz oldu\u011funu varsayarak, bu iki vekt\u00f6r\u00fcn \u00e7apraz \u00e7arp\u0131m\u0131n\u0131 a\u015fa\u011f\u0131daki \u015fekilde hesaplayabiliriz: \u00c7apraz \u00e7arp\u0131m = [(A 2 *B 3 ) \u2013 (A 3 *B 2 ), (A 3 *B [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-2711","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - 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